Precalculus Exam 2

Question

The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 5 and a root of multiplicity 1 at x=-3. The y-intercept is y= -45. Find a formula

Answer 1

If the roots are x = 5, x = 5, and x = -3 then the polynomial has factors of (x - 5)(x - 5)(x + 3)

So, since the polynomial can have a multiplier and still have the same zeros, we would say:

P(x) = a(x - 5)(x - 5)(x + 3) where a is the multiplier.

Since you were given a point (y intercept= -45 or the point is (0, -45), just plug in the point as the "x" and "P(x)" into P(x) = a(x - 5)(x - 5)(x + 3) and solve for "a". Then multiply the results out if necessary.