Question

For what values of k does the quadratic equation 4x2 − 12x − k = 0 has no real roots?

Answer 1

We have been given the quadratic equation:

`4x^2 - 12x - k = 0`

To have no real roots means discriminant should be less than zero.

`D = b^2 - 4ac`

`b^2 - 4ac < 0`

Plugging the values in the formula of discriminant

`(-12)^2 - 4(4)(-k) < 0`

`144 + 16k < 0`

`k < -9`

Therefore, for k<-9 the quadratic equation will have no real roots.