Zeros of Polynomial Functions

Question

construct a polynomial function of least degree possible using the given information.

Real roots: –2,1/2 (with multiplicity 2) and (−3,f(−3))=(−3,5)

Answer 1

From the given real roots (and their multiplicities) we can construct a polynomial in factored form with a leading coefficient, a, which we can then solve for using the given point as follows:

f(x) = a(x + 2)(2x - 1)²

f(-3) = a (-1)(-7)² = 5

a = - 5/49

f(x) = - 5/49(x + 2)(2x - 1)²