Question

If roots of the quadratic equation `x^2 - ksqrt(3)x + 2 = 0` are real and equal, then value of k is ______.

Options

• –2

• `sqrt(8/3)`

• 1

• 2

Answer 1

If roots of the quadratic equation `x^2 - ksqrt(3)x + 2 = 0` are real and equal, then value of k is `underlinebb(sqrt(8/3))`.

Explanation:

For a quadratic equation ax² + bx + c = 0 to have real and equal roots, its discriminant must be zero.

Discriminant (D) = b² – 4ac = 0.

Here, a = 1, b = `-ksqrt(3)`, c = 2

Substitute values into the discriminant formula:

`(-ksqrt(3))^2 - 4(1)(2) = 0`

3k² – 8 = 0

3k² = 8

`k^2 = 8/3`

`k = ± sqrt(8/3)`

The value of k is `sqrt(8/3)`.