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