Question

Write a polynomial equation of degree 3 such that two of its roots are 2 and an imaginary number.

Answer 1

Hey!!

It is given that a polynomial is having a degree of 3 and its roots are 2 and one root is imaginary. So,

One root (2) = (x-2)

Imaginary root = (x+i),(x-i)

According to the question, the polynomial is having the degree of 3 so,

(x-2)(x+i)(x-i)

Solving these roots further we'll get,

(x-2)(x²+xi-xi-i²)

(x-2)(x²+i²)

We know that i²= -1 so,

(x³-x-2x²-2)

x³-2x²+x-2.