Question

Solve the following quadratic equation:

x² – 4x + 13 = 0

Answer 1

The given equation is x² – 4x + 13 = 0

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

a = 1, b = –4, c = 13

Discriminant = b² – 4ac

= (– 4)² – 4 × 1 × 13

= 16 – 52

= –36 < 0

So, the given equation has complex roots.

These roots are given by

x = `(-b +- sqrt(b^2 - 4 ac))/(2 a)`

= `(-(- 4) +- sqrt(- 36))/(2 xx 1)`

= `(4 +- 6 i)/2`

= 2 ± 6i

∴ The roots of the given equation are 2 + 6i and 2 – 6i.