Find a polynomial of degree 4 with -2 as a zero of multiplicity 2 and 0 and 3 as zeros of multiplicity 1.
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1 Answer

A zero of -2 with multiplicity 2 means (x+2)² is a factor.

A polynomial is therefore (x+2)²(x(x-3))=(x²+4x+4)(x²-3x)=

x⁴+4x³ +4x²

   -3x³-12x²-12x=

x⁴+x³-8x²-12x or any multiples of this polynomial.

 

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