Question

The value(s) of k for which the quadratic equation 5x² − 9kx + 5 = 0 has real and equal roots is/are ______.

पर्याय

• `-10/9`

• `±9/10`

• `10/9`

• `±10/9`

Answer 1

The value(s) of k for which the quadratic equation 5x² − 9kx + 5 = 0 has real and equal roots is/are `±10/9`.

Explanation:

We know that the quadratic equation has real and equal roots, if its discriminant is equal to zero, i.e. b² − 4ac = 0

Given, quadratic equation is 5x² − 9kx + 5 = 0

Here, a = 5, b= −9k and c = 5

So, b² − 4ac = 0

∴ (−9k)² − 4(5)(5) = 0

∴ 81k² − 100 = 0

∴ k² = `100/81`

∴ k = `±10/9`

Hence, the values of k are `±10/9`.