Question

Find the equation for a polynomial f(x)that satisfies the following:Degree 5• Root of multiplicity 2 at x = -2• Root of multiplicity 1 at x = 2• Root of multiplicity 2 at x = -2y-intercept of (0, -64)

Answer 1

y = 2(x+2)⁴(x-2)

Step-by-step explanation:

If b and c are roots of an equation, the equation can be written as:

y = a(x-a)(x-b)

So, this equation can be written as:

y = a(x-(-2))²(x-2)(x-(-2))²

y = a(x+2)²(x-2)(x+2)²

y = a(x+2)⁴(x-2)

Now, let's find "a" using the y-intercept. To do it, let's substitute the point and isolate a.

y = a(x+2)⁴(x-2)

-64 = a(2)⁴(-2)

-64 = a*16*(-2)