Question

If the roots of the quadratic equation `sqrt3x^2 - kx + 2sqrt3 = 0` are real and equal, then the value (s) of k is/are ______.

Options

• `±sqrt24`

• 0

• 4

• −5

Answer 1

If the roots of the quadratic equation `sqrt3x^2 - kx + 2sqrt3 = 0` are real and equal, then the value (s) of k is/are `bbunderline(±sqrt24)`.

Explanation:

`sqrt3x^2 - kx + 2sqrt3 = 0`

a = `sqrt3, b = −k, c = 2sqrt3`

b² − 4ac = 0

`(−k)^2 - 4(sqrt3 xx 2sqrt3) = 0`

k² − 4(2 × 3) = 0

k² − 4(6) = 0

k² − 24 = 0

k² = 24

k = `±sqrt24`