Question

Write a polynomial function f of least degree that has real coefficients, a leading coefficient of1 and the following zeros: -3 and 4i

Answer 1

Let the polynomial function be f(x)

Given that f(x) has two zeroes -3 and 4i

Then, f(x) can be written as

f(x)=[x-(-3)](x-4i)

On multiplying,

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

=x^2+(3-4i)x-12i

The leading coefficient is 1 and the roots are -3 and 4i