Question

Solve the following quadratic equation.

x² − 4x + 13 = 0

Answer 1

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 x 1 x 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(1))`

= `(4 ± 6"i")/2`

= `4/2 ± (6"i")/2`

= 2 ± 3i

∴ the roots of the given equation are 2 + 3i and 2 − 3i.