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:

4x² – 12x – k = 0

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

D = b² – 4ac

b² – 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.