Find a polynomial function Px of degree 3 whose real zeros a

Find a polynomial function P(x) of degree 3 whose real zeros are: 2 (multiplicity 1), -3 (multiplicity 2) and leading coefficient -5 (Write p(x) on an expanded form.)

Solution

Zeroes are   2 with a multiplicity of 1   and     -3 with a multiplicity of 2

Therefore required polynomial is

P(x)=-5(x-2)(x+3)²   =   -5x³-20x² +15x +90