How do you write a polynomial in standard form given zeros 1 (multiplicity 2), -2 (multiplicity 3)?

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Answer 1 · 2016-05-26T09:35:22

#x^5+4x^4+x^3-10x^2-4x+8=0#

If #{alpha,beta,gamma,delta,..}# are the zeros of a function, then the function is

#(x-alpha)(x-beta)(x-gamma)(x-delta)...=0#

Here zeros are #1# (multiplicity #2#) and #-2# (multiplicity #3#), hence function is

#(x-1)(x-1)(x+2)(x+2)(x+2)=0# or

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

#(x^2-2x+1)(x^3+6x^2+12x+8)=0# or

#x^2(x^3+6x^2+12x+8)-2x(x^3+6x^2+12x+8)+1(x^3+6x^2+12x+8)=0#

#x^5+6x^4+12x^3+8x^2-2x^4-12x^3-24x^2-16x+x^3+6x^2+12x+8=0#

#x^5+4x^4+x^3-10x^2-4x+8=0#