Question

He polynomial of degree 5, p ( x ) p(x) has leading coefficient 1, has roots of multiplicity 2 at x = 4 x=4 and x = 0 x=0, and a root of multiplicity 1 at x = − 4 x=-4 find a possible formula for p ( x ) p(x).

Answer 1

root of x = 4 means (x - 4) is a factorMultiplicity of two means that (x - 4) is used twice root of x= -4 means that (x+ 4) is a factormultiplicity of 1 means it is used once so y = a (x-4) (x-4) (x + 4)y = a (x^3 - 4x2 - 16x + 64)
Thus, any polynomial with these zeroans d as a minimum these multiplicities will be a multiple (scalar or polynomial) of this P(x).