Question

Find a cubic polynomial in standard form with real coefficients, having the given zeros.

0 and 4+ 3i
P(x)=(Simplify your answer.)

Answer 1

P(x) = x^3 - 8x^2 + 25x

Explanation:

The roots of p(x) are 0, 4+3i, and because of the conjugate, 4-3i is also a root.

so p(x) = (x-0)(x-(4+3i))(x-(4-3i))

= x((x-4)+3i)((x-4)-3i)

= x[(x-4)^2-(3i)^2]

=x(x^2-8x+16+9)

x^3-8x^2+25x