Give an expression for f(x) using only Real-valued coefficients, having degree 4, passing through the point (-3,-850), with roots x=-8, x=-2, and x=2+3i.

Question

final answer should not have any i's.

f(x)= _______ is a polynomial of degree 4 with the given roots and passes through (-3,-850).

Answer 1

By conjugate zeros theorem x = 2 - 3i also zero. Because f(x) = a(x + 2)(x + 8)(x - 2 + 3i)(x - 2 - 3i);

f(x) = a(x + 2)(x + 8)(x² - 4x + 13); f(-3) = a(- 3 + 2)(- 3 + 8)(9 + 12 + 13) = - 850; a = 5

f(x) = 5(x + 2)(x + 8)(x² - 4x + 13)