Write a polynomial function that satisfies roots of multiplicity.

Question

write a polynomial function that satisfies roots of multiplicity 2 at x = -3 and x = 2 and a root of multiplicity 1 at x = -2. Y-intercept (0,4)

Answer 1

Multiplicity of 2 at x = -3 means it has a factor of (x + 3)²

Multiplicity of 2 at x = 2 means it has a factor of (x - 2)²

Multiplicity of 1 at x = -2 means it has a factor of (x + 2)

 

y(x) = A(x + 3)²(x - 2)²(x + 2), A ≠ 0 

 

To find A, use the given point (0,4).

 

4 = A(0 + 3)²(0 - 2)²(0 + 2) = A*9*4*2

 

1 = 18A

 

A = 1/18

 

y(x) = (1/18)(x + 3)²(x - 2)²(x + 2)