Question

Find the values of k for which the roots are real and equal in each of the following equation:

4x² + kx + 9 = 0

Answer 1

The given quadric equation is 4x² + kx + 9 = 0, and roots are real and equal

Then find the value of k.

Here, a = 4, b = k and c = 9

As we know that D = b² - 4ac

Putting the value of a = 4, b = k and c = 9

= (k)² - 4 x (4) x (9)

= k² - 144

The given equation will have real and equal roots, if D = 0

Thus,

k² - 144 = 0

k² = 144

`k=sqrt144`

k = ± 12

Therefore, the value of k = ± 12.