Question

Write a quadratic equation with 2+7i and 2-7i as its solutions

Answer 1

Solutions of a quadratic equation is 2 + 7i and 2 - 7i

From factor theorem

When f (c ) = 0 then x - c is a factor of polynomial.

2 + 7i and 2 - 7i are solutions of quadratic equation.

Quadratic equation have two solutions.

Therfore [x - (2 + 7i)][x - (2 - 7i)] = 0

(x-2)² -(7i)² =0                               (Since (a+b)(a-b) = a² - b² )

X² - 4x +4 - 7² (i) ² =0

The equation is