a 6th degree polynominal with a root of multiplicity 2 at x=3 and a root of multiplicity 4 at x=-2, can be written as the function y=(x-3)^a(x-b)^c where:

Question

A= _____

B=_____

C= _____

The y intercept of this polynominal is (0,_)

Answer 1

Since the zero of 3 has a multiplicity of 2, it would be (x-3)² would be the first factor. The second factor has a zero of -2 and a multiplicity of 4, the factor would be (x-(-2))⁴. Putting these together:

(x-3)²(x-(-2))⁴

A=2

B=-2

C= 4

To find the y intercept, set x=0

(0-3)²(0+2)⁴

(-3)²(2)⁴ = (9)(16) = 144

y intercept: (0,144)

Answer 2

Roots: 3,3,-2,-2,-2,-2

y=f(x)=(x-3)² *(x-(-2))⁴ = (x-3)² *(x+2)⁴

So, A=2, B=-2, C=4

The y intercept of this polynomial when x=0.

f(0)=(0-3)² *(0+2)⁴ = 9*16 = 144

This occurs at (0, 144)