Question

For what value of of k the quadratic equation 4x2-12x-k have no real roots.

Answer 1

Answer:

k < -9

Step-by-step explanation:

As p(x) = 4x² - 12x - k = 0 has no real roots, the discriminant is less than 0.

$a=4 \\ b=-12 \\ c=-k$

$b^2-4ac<0 \\ \\ (-12)^2-(4 \times 4 \times -k)<0 \\ \\ 144-(-16k)<0 \\ \\ 144+16k<0 \\ \\ 16k<-144 \\ \\ k<-144/16 \\ \\ k<\bold{-9}$

So p(x) has no real roots if the value of k is less than -9.