Pre-calculus problem

Question

The polynomial of degree , , has a root of multiplicity  at  and a root of multiplicity  at . The -intercept is .Find a formula for .

Answer 1

Since P(x) has a root of multiplicity 2 at x = 5, you will need to have 2 parentheses with (x-5)

Since P(x) has a root of multiplicity 1 at x = -3, you will need 1 parentheses with (x+3)

So P(x) = a* (x-5)*(x-5)*(x+3)

How do you find a? You're told of the y-intercept, which means the point (0, -37.5).

Replace P(x) by -37.5 and x by 0 ---> -37.5 = a *(-5)*(-5)*(3)

-37.5 = a*75

Divide both sides by 75 ---> a = -0.5 = -1/2

so P(x) = -0.5* (x-5)*(x-5)*(x+3)