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=−37.5; Find a formula for P(x).

Answer 1

P(x) = a(x -5)²(x + 3). To get a we use y-intercept P(0) = - 37.5.

So, a(0 - 5)²(0 + 3) = - 37.5, 75a = - 37.5, a = - 0.5. P(x) = - 0.5(x - 5)²(x + 3) = - 0.5(x² - 10x + 25)(x + 3) = - - 0.5x³ + 3.5x² + 2.5x - 37.5