Question

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

9x² - 24x + k = 0

Answer 1

The given quadric equation is 9x² - 24x + k = 0, and roots are real and equal

Then find the value of k.

Here, a = 9, b = -24 and c = k

As we know that D = b² - 4ac

Putting the value of a = 9, b = -24 and c = k

= (-24)² - 4 x (9) x (k)

= 576 - 36k

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

Thus,

576 - 36k = 0

36k = 576

k = 576/36

k = 16

Therefore, the value of k = 16.