Question

State how many imaginary and real zeros the function has.
f(x) = x3 + 5x2 - 28x - 32

Answer 1

2

Answer 2

f(0)=-32
f(big positive number)=very big positive number
So it must have at least one real root. Since the polynomial has real coefficients, it must be the case that all complex roots come in conjugate pairs, or else the polynomial would have complex coefficients. So it is either one real root or three real roots for this polynomial. Find the first root and perform polynomial division to get a quadratic factor. If the quadratic can be factored over the reals the polynomial has three real roots, else one real root.

Answer 3

It shouldn't take you too long to find the first root by trial and error.