Polynomial of degree

Question

The polynomial of degree 4,  has a root of multiplicity 2 at  and roots of multiplicity 1 at  and . It goes through the point .Find a formula for .

P(x) = ?

Answer 1

(X-3)2X(X+2), when substitute X with 5, we get 140, 56 / 140 = 0.4, so

P(X) = 0.4 (X-3)²X(X+2),

Answer 2

Use factored form of the polynomial (since we are given its roots):

P(x) = a·x(x + 2)(x - 3)² , where a represents the lead (quartic) coefficient. We use the given pt to find a:

P(5) = a·5·7·4 = 56. a = 2/5

P(x) = 2/5·x(x + 2)(x - 3)²