Question

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

(k + 1)x² + 2(k + 3)x + (k + 8) = 0

Answer 1

The given quadric equation is (k + 1)x² + 2(k + 3)x + (k + 8) = 0, and roots are real and equal

Then find the value of k.

Here,

a = (k + 1), b = 2(k + 3) and c = (k + 8)

As we know that D = b² - 4ac

Putting the value of a = (k + 1), b = 2(k + 3) and c = (k + 8)

= (2(k + 3))² - 4 x (k + 1) x (k + 8)

= (4k² + 24k + 36) - 4(k² + 9k + 8)

= 4k² + 24k + 36 - 4k² - 36k - 32

= -12k + 4

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

-12k + 4 = 0

12k = 4

k = 4/12

k = 1/3

Therefore, the value of k = 1/3.