Question

Find a polynomial of the specified degree that satisfies the given conditions.

Degree 4; zeros −3, 0, 1, 4; coefficient of x3 is 4
f(x) =?

Answer 1

f(x) = Cx(x + 3)(x - 1)(x - 4)

= C(x² + 3x)(x² - 5x + 4)

= C(x⁴ - 5x³ + 4x² + 3x³ - 15x² + 12x)

= C(x⁴ - 2x³ - 9x² + 12x)

C = -2, so f(x) = -2x⁴ + 4x³ + 18x² - 24