Question

The roots of quadratic equation `3 x^2 − 4sqrt3x + 4` = 0 are ___________.

Options

• not real

• real and equal

• rational and distinct

• irrational and distinct

Answer 1

The roots of quadratic equation `3 x^2 − 4sqrt3x + 4` = 0 are real and equal.

Explanation:

`3 x^2 − 4sqrt3 + 4`

Comparing equation with ax² + bx + c = 0

a = 3, b = `− 4sqrt3`, c = 4

∴ D = b² − 4ac

= `(−4 sqrt3)^2 − 4 xx 3 xx 4`

= 48 − 48

Since D = 0,

The given equation has two equal real roots.