Question

Write a polynomial of least degree with zeros 2 and -4i

Answer 1

Given data:

The first root of the polynomial is x=2.

The second root of the polynomial is x=-4i.

The imaginary roots are always in pair, the third root of the polynomial is,

x=+4i.

The expression for the polynomial is,

f(x)=(x-2)(x+4i)(x-4i)

=(x-2)(x^2-16i^2)

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

=x^3+16x-2x^2-32.

Thus, the polynoial of least degree is x^3-2x^2+16x-32.