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