# Rational Zeros

### Topic Page

Rational Zeros### Questions

- What is the rational zeros theorem?
- How do I find all the rational zeros of function?
- What is a rational zero?
- How do I find all the rational zeros of a function like #f(x)=x^3-7x-6#?
- How do you find all the rational zeros of a polynomial function?
- How do I find all the rational zeros of #p(x)=x^3-12x-16#?
- What are all the rational zeros of #x^3-7x-6#?
- What are all the rational zeros of #2x^3-15x^2+9x+22#?
- What are the rational zeros for #x^3-3x^2-4x+12#?
- What are the rational zeros of a polynomial function?
- What is the rational zeros test?
- How do you use the rational zero theorem to list all possible rational zeros for the given function #f(x)=x^3-14x^2+13x-14#?
- How do you use the rational root theorem to find the roots of #x^3-x^2-x-3=0#?
- How do you use the rational root theorem to list all possible rational roots?
- How do you use the rational root theorem to find the roots of #2x^3 + 7x^2 - 77x - 40#?
- How do you use the rational root theorem to find the roots of #x^3+2x-9=0#?
- How do you use the rational root theorem to find the roots of #x^4-x^3-2x^2-4x-24#?
- How do you use the rational root theorem to find the roots of #314x^3+1099x^2-1413#?
- How do you use the rational root theorem to find the roots of #2x^4 + 3x^3 - 7x^2 + 3x - 9 = 0 #?
- How do you use the rational root theorem to find the roots of #f(x)=x^3+x^2-8x-6 #?
- How do you use the rational root theorem to find the roots of #x^3 + 6x^2 - x - 10 = 0#?
- How do you use the rational root theorem to find the roots of #x^3-7x^2+10x-2=0#?
- How do you use the rational root theorem to find the roots of #x^4 + x^3 -2x^2 + 0x -290 = 0#?
- How do you use the rational root theorem to find the roots of #P(x) = x^4 - x^3 - 15x^2 + 3x + 36#?
- How do you use the rational root theorem to find the roots of #x^3 + 9x^2 - x + 8 = 0#?
- How do you use the rational root theorem to find the roots of #2x^3 - 4x^2 + x - 7#?
- How do you use the rational root theorem to find the roots of #8y^4 - 6y^3 + 17y^2 - 12y + 2 = 0#?
- How do you use the rational root theorem to find the roots of #P(x) = 0.25x^2 - 12x + 23#?
- How do you use the rational root theorem to find the roots of #5x^4 + 9x^3 + 5x^2 + 2x + 4 = 0#?
- How do you use the rational root theorem to find the roots of #3x^4 + 5x^3 + 3x^2 - 7x + 9 = 0#?
- How do you use the rational root theorem to find the roots of #x^4 + 2x + 2 = 0#?
- How do you use the rational root theorem to find the roots of #x^4 + 3x^3 - x^2 - 9x - 6 = 0#?
- How do you use the rational root theorem to find the roots of #2x^4 -7x^3 -35x^2 +13x +3#?
- How do you use the rational root theorem to find the roots of # f(x) = 3x^3 + 7x^2 + 11x + 5#?
- How do you use the rational root theorem to find the roots of #3x^3 + 3x^2-2x + 15 = 0#?
- How do you use the rational root theorem to find the roots of #F(x) = 4x^3 - 6x^2 + 9x + 10#?
- How do you use the rational root theorem to find the roots of #x^3 + 2x^2 + 3x + 6 = 0 #?
- How do you use the rational root theorem to find the roots of #x^4 – 7x^2 + 12 = 0#?
- How do you use the rational root theorem to find the roots of #r(x) = 5t^3 – 8t^2 + 7t + 2#?
- How do you use the rational root theorem to find the roots of #3x^3 - kx^2 - 16x + 12 = 0#?
- How do you use the rational root theorem to find the roots of #f(x)=x^4-x-4#?
- How do you use the rational root theorem to find the roots of # f(x)=x^5-3x^2-4#?
- How do you use the rational root theorem to find the roots of #x^3 – x^2 – x – 3 = 0#?
- How do you use the rational root theorem to find the roots of #x^3-x^2+2x-2#?
- How do you use the rational root theorem to find the roots of #4x^3 - 3x^2 + x - 2 = 0#?
- How do you use the rational root theorem to find the roots of #3x^4-10x^3-24x^2-6x+5#?
- How do you use the rational root theorem to find the roots of #F(x) = 8x^3 - 3x^2 + 5x + 15 #?
- How do you use the rational root theorem to find the roots of # f(x) = x^3-4x^2-2x+8#?
- How do you use the rational root theorem to find the roots of #2x^3 - 9x^2 - 11x +8 = 0#?
- How do you use the rational root theorem to find the roots of #x^3-9x^2+14x=48#?
- How do you use the rational root theorem to find the roots of #x^3 – x^2 – x – 3 = 0#?
- How do you use the rational root theorem to find the roots of #3x^4+2x^3-9x^2-12x-4=0#?
- How do you use the rational root theorem to find the roots of #10x^4 + x^3 + 7x^2 + x -3 = 0#?
- How do you use the rational root theorem to find the roots of #x^4 - 7x^2 + 12 = 0#?
- How do you use the rational root theorem to find the roots of #8x^3-3x^2+5x+15#?
- How do you find the rational roots of #x^4+5x^3+7x^2-3x-10=0#?
- How do you find the rational roots of #x^4+3x^3+3x^2-3x-4=0#?
- How do you use the Rational Root Theorem to find all the roots of #x^3 + 9x^2 + 19x – 4 = 0#?
- How do you use the Rational Root Theorem to find all the roots of #2x^3 – x^2 + 10x – 5 = 0 #?
- How many real and complex roots does #3x^4+4x^3+x-1 = 0# have?
- How do you find the x- and y-intercepts of #f(x) = (4 - x) / x#, then determine whether the graph of f touches or crosses the x-axis at the x-intercept?
- How do you solve #(2-x)^4+(3-x)^4-(5-x)^4 = 0# ?
- How do you define a cubic function with zeros #r_1, r_2, r_3# such that #r_1+r_2+r_3 = 3#, #r_1r_2+r_2r_3+r_3r_1 = -1#, #r_1r_2r_3 = -3# ?
- #f(x) = 2x^4-3x^3-5x^2+9x-3# Given that #sqrt(3)# forms two of the roots, find all the roots of the polynomial?
- What are all the possible rational zeros for #f(x)=3x^2+2x-1#?
- What are all the possible rational zeros for #f(x)=x^6-64#?
- What are all the possible rational zeros for #f(x)=x^2+8x+10#?
- What are all the possible rational zeros for #f(x)=5x^3-2x^2+20x-8#?
- What are all the possible rational zeros for #f(x)=4x^5-2x^4+30x^3-15x^2+50x-25#?
- What are all the possible rational zeros for #f(x)=5x^4+32x^2-21#?
- What are all the possible rational zeros for #f(x)=2x^4-9x^2+7#?
- What are all the possible rational zeros for #f(x)=x^3+x^2-5x+3# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3-13x^2+23x-11# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3+4x^2+5x+2# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=5x^3+29x^2+19x-5# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=4x^3-9x^2+6x-1# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=3x^3+11x^2+5x-3# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=5x^4-46x^3+84x^2-50x+7# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=3x^4-10x^3-24x^2-6x+5# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=2x^3+9x^2+19x+15# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=2x^3+x^2+8x-21# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=2x^3+x^2-2x-1# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=5x^3-11x^2+7x-1# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=5x^3+x^2-5x-1# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3+3x^2-x-3# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^4+2x^2-8# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^5+2x^4+14x^3+26x^2+40x+80# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^4-7x^2+10# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3+9x^2+15x+7# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=5x^3-31x^2+31x-5# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3-10x^2+16x+15# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=2x^3-3x^2+1# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=3x^3-8x^2-2x-3# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3+x^2-19x+5# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3+5x^2-11x-6# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=2x^3+5x^2+4x+1# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3+13x^2+38x+24# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=3x^3+5x^2-11x+3# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=2x^3-5x^2+4x-1# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=3x^3-x^2-3x+1# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=3x^3-11x^2+5x+3# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3+11x^2+35x+33# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=3x^3-7x^2+29x-9# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=5x^3-9x^2-12x-2# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3+3x^2+x-2# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=2x^3-8x^2+15x-27# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=5x^3-9x^2+3x+1# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3+5x^2-48x-10# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3-9x^2+15x-2# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3-4x^2-3x+14# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3-6x^2+7x+4# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^4-3x^3-6x^2+6x+8# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=2x^3-3x^2-4x+6# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=2x^4-7x^3-2x^2-7x-4# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3+x^2-8x-6# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=2x^4-6x^2+5x-15# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=3x^5-6x^4+2x^2-6x+12# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=8x^3-2x+24# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=10x^3-15x^2-16x+12# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=-6x^3+5x^2-2x+18# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=4x^4-16x^3+12x-30# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=4x^4+3x^3-2x^2+5x-12# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^5-6x^4+12x^2-8x+36# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3-4x^2-14# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=2x^3-4x+8# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=4x^5+4x^2-9# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=x^3+2x^2-5x-6# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=2x^3+x^2+8x+4# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=2x^4-13x^3-34x^2+65x+120# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=4x^4+19x^2-63# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=4x^4-17x^2+4# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=32x^3-52x^2+17x+3# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=6x^3-x^2-13x+8# and how do you find all zeros?
- What are all the possible rational zeros for #f(x)=4x^3+7x^2-11x-18# and how do you find all zeros?
- What are all the possible rational zeros for #y=x^3+x^2-9x+7# and how do you find all zeros?
- What are all the possible rational zeros for #y=x^4-x^3-4x^2+2x+4# and how do you find all zeros?
- What are all the possible rational zeros for #y=2x^5-x^4-26x^3+13x^2+72x-36# and how do you find all zeros?
- What are all the possible rational zeros for #y=12x^2-28x+15# and how do you find all zeros?
- What are all the possible rational zeros for #y=21x^2+11x-40# and how do you find all zeros?
- What are all the possible rational zeros for #y=x^3-5x^2+17x-13# and how do you find all zeros?
- What are all the possible rational zeros for #y=4x^3+12x^2+x+3# and how do you find all zeros?
- What are all the possible rational zeros for #y=3x^3+10x^2+4x-8# and how do you find all zeros?
- What are all the possible rational zeros for #y=30x^3-x^2-6x+1# and how do you find all zeros?
- What are all the possible rational zeros for #y=x^4-2x^3-21x^2+22x+40# and how do you find all zeros?
- What are the roots of #8x^3-7x^2-61x+6=0# ?
- What are the possible rational roots of #x^3-4x^2+x+2=0# and then determine the rational roots?
- What are the possible rational roots of #2x^3+3x^2-8x+3=0# and then determine the rational roots?
- What are the possible rational roots of #x^3-2x^2+x+18=0# and then determine the rational roots?
- What are the possible rational roots of #x^4-5x^3+9x^2-7x+2=0# and then determine the rational roots?
- What are the possible rational roots of #x^3-5x^2-4x+20=0# and then determine the rational roots?
- What are the possible rational roots of #2x^4-x^3-6x+3=0# and then determine the rational roots?
- What are the possible rational roots of #6x^4+35x^3-x^2-7x-1=0# and then determine the rational roots?
- How do you find the number of possible positive real zeros and negative zeros then determine the rational zeros given #f(x)=8x^3-6x^2-23x+6#?
- How do you find the number of possible positive real zeros and negative zeros then determine the rational zeros given #f(x)=x^3+7x^2+7x-15#?
- How do you find the number of possible positive real zeros and negative zeros then determine the rational zeros given #f(x)=x^3-7x-6#?
- How do you find the number of possible positive real zeros and negative zeros then determine the rational zeros given #f(x)=x^3-2x^2-8x#?
- How do you find the number of possible positive real zeros and negative zeros then determine the rational zeros given #f(x)=x^3+3x^2-10x-24#?
- How do you find the number of possible positive real zeros and negative zeros then determine the rational zeros given #f(x)=10x^3-17x^2-7x+2#?
- How do you find the number of possible positive real zeros and negative zeros then determine the rational zeros given #f(x)=x^4+2x^3-9x^2-2x+8#?
- How do you find the number of possible positive real zeros and negative zeros then determine the rational zeros given #f(x)=x^4-5x^2+4#?
- How do find all zeros of the function?
- How do you find the rational roots of #x^4+8x^3+7x^2-40x-60=0#?
- Can you use mathematical induction to prove that the sequence defined by #t_1=6# , #t_(n+1)= t_n/(3n# for all #n in ZZ^+# can be written as #t_n=18/(3^n(n-1)!# for all #n in ZZ^+#?
- Can you use mathematical induction to prove that #t_n >= t_(n-1)# for all #n in ZZ^+# for a sequence with the general term: #t_n=(3n+5)/(n+2), n in ZZ^+#?
- How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=x^3-2x^2-5x+6#?
- How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=x^4+2x^3-12x^2-40x-32#?
- How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=x^4-9x^2-4x+12#?
- How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=x^3+4x^2-11x+6#?
- How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=x^3-7x^2+x-7#?
- How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=-2x^3+19x^2-49x+20#?
- How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=-17x^3+5x^2+34x-10#?
- How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=36x^4-12x^3-11x^2+2x+1#?
- How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=3x^3+3x^2-11x-10#?
- How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=2x^4+x^3-7x^2-3x+3#?
- Question #1d5ec
- How do you solve #-5x^2-2x-4 = 0# ?
- How many roots do the following equations have? -12x^2 -25x +5 +x^3 =0
- What are the possible rational zeros of #P(x) = 4x^4+19x^3-x^2+19x-5# ?