Question

Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:

`3x^2 - 4sqrt3x + 4 = 0`

Determine the nature of the roots of the following quadratic equation:

`3x^2 - 4sqrt3x + 4 = 0`

Answer 1

`3x^2 - 4sqrt3x + 4 = 0`

Comparing it with ax² + bx + c = 0, we get

a = 3, b = `-4sqrt3`  and c = 4

Discriminant = b² - 4ac

= `(-4sqrt3)^2 - 4(3)(4)`

= 48 - 48

= 0

As b² - 4ac = 0,

Therefore, real roots exist for the given equation and they are equal to each other.

And the roots will be `(-b)/(2a) `

i.e, `(-(-4)sqrt3)/(2xx3) and (-(-4sqrt3))/(2xx3)`

= `(4sqrt3)/(2sqrt3 xx sqrt3) and (4sqrt3)/(2sqrt3 xxsqrt3)`

Therefore, the roots are `2/sqrt3 and 2/sqrt3.`