Question

Discuss the nature of the roots of the following equation without actually solving it:

`2x^2 - 2sqrt(6)x + 3 = 0`

Answer 1

Comparing `2x^2 - 2sqrt(6)x + 3 = 0` with ax² + bx + c = 0 we get,

a = 2, b = `-2sqrt(6)` and c = 3

We know that,

Discriminant (D) = b² – 4ac

= `(-2sqrt(6))^2 - 4 xx 2 xx 3`

= (4 × 6) – 24

= 24 – 24

= 0

Since, b is irrational and discriminant equals to zero.

Hence, the roots are irrational and equal.