Write a simplified quartic equation with integer coefficients and positive leading coefficients as small as possible, whose single roots are #-1/3# and 0 and has a double root as 0.4?

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Answer 1 · 2017-10-01T01:22:36

#75x^4-35x^3-8x^2+4x=0#

We have roots of:

#x=-1/3, 0, 2/5, 2/5#

We can then say:

#x+1/3=0, x=0, x-2/5=0, x-2/5=0#

And then:

#(x+1/3)(x)(x-2/5)(x-2/5)=0#

And now starts the multiplying:

#(x^2+1/3x)(x-2/5)(x-2/5)=0#

#(x^2+1/3x)(x^2-4/5x+4/25)=0#

#x^4+1/3x^3-4/5x^3-4/15x^2+4/25x^2+4/75x=0#

#75x^4+25x^3-60x^3-20x^2+12x^2+4x=0#

#75x^4-35x^3-8x^2+4x=0#