Question

The nature of the roots of the equation, `3x^2 - 4sqrt(3)x + 4 = 0` is ______.

Options

• real and equal

• irrational and unequal

• rational and unequal

• imaginary and unequal

Answer 1

The nature of the roots of the equation, `3x^2 - 4sqrt(3)x + 4 = 0` is real and equal.

Explanation:

For `3x^2 - 4sqrt(3)x + 4 = 0`, 

a = 3, b = `-4sqrt(3)`, c = 4.

Discriminant D = b² – 4ac

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

= 16(3) – 48

= 48 – 48

= 0

So, the roots are real and equal.