Question

Find a degree 3 polynomial with coefficient of x^3 equal to 1 and zeros -2, -2 i and 2 i

Answer 1

well the complex roots of x = -2i, 2i means the quadratic is

\[x^2 = -4 ~~~~~~or~~~~~~~x^2 + 4 = 0\]

the the general form is

\[f(x) = a(x^2 + 4)(x + 2) \]

you are told the coefficient of the leading term is 1 so a = 1

so you need to expand/distribute

\[f(x) = (x^2 + 4)(x + 2)\]

to find the polynomial.

Answer 2

Thank you!