Question

Find the nature of roots of the quadratic equation `x^2 + 4x - 3sqrt(2) = 0`.

Answer 1

Given equation: `x^2 + 4x - 3sqrt(2) = 0`

Here, a = 1, b = 4, c = `-3sqrt2`

Discriminant (D) = b² − 4ac

= `4^2 - 4 xx 1 xx -3sqrt2`

= `16 + 12sqrt(2)`

Since `16 + 12sqrt(2) > 0`

D > 0, so roots are real and unequal.

The roots are real and distinct (unequal).