# For What Values of K Does the Quadratic Equation 4x2 − 12x − K = 0 Has No Real Roots? - Mathematics

Sum

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

#### Solution

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.

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