Question

Roots of the quadratic equation x² - 2ix + 3 = 0 are:
1. 3i, -i
2. 3i, i
3. ±3i
4. -3i, -i

Answer 1

Correct Answer - Option 1 : 3i, -i

Concept:

If ax² + bx + c = 0 be any quadratic equation then roots of the equation can be determined by, \(x=\frac{-b±\sqrt{b^2-4ac}}{2a}\)              -----(i)

Calculation:

Given, quadratic equation is x2 - 2ix + 3 = 0

on comparing with standard equation we get, a= 1, b = -2i, c = 3

by using equation (i),

⇒ \(x=\frac{-(-2i)±\sqrt{(-2i)^2-4✕1✕3}}{2✕1}\)

⇒ \(x=\frac{2i±\sqrt{4i^2-12}}{2}\)

⇒ \(x=\frac{2i±\sqrt{-16}}{2}\)

⇒ \(x=\frac{2i±4i}{2}\)

⇒ \(x = 3i, -i\)