Question

Solve the following quadratic equation:

x² – (5 – i) x + (18 + i) = 0

Answer 1

Given equation is x² – (5 – i)x + (18 + i) = 0

Comparing with ax² + bx + c = 0, we get

a = 1, b = -(5 – i), c = 18 + i

Discriminant = b² – 4ac

= [-(5 – i)]² – 4 × 1 × (18 + i)

= 25 – 10i + i² – 72 – 4i

= 25 – 10i – 1 – 72 – 4i ……[∵ i = -1]

= -48 – 14i

So, the given equation has complex roots.

These roots are given by

Equating real and imaginary parts, we get