If the equation x^{2} + 2(k + 2)x + 9k = 0 has equal roots then k = ?

Given that the equation x^{2} + 2(k + 2)x + 9k = 0 has equal roots.

a = 1 b = 2(k + 2) c = 9k

D = b^{2} - 4ac = 0

(2k + 4)^{2} - 4.1.9k = 0

4k^{2} + 16 + 16k - 36k = 0

4k^{2} - 20k + 16 = 0

k^{2} - 5k + 4 = 0

Using the splitting middle term - the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = 1 b = - 5 c = 4

= 1.4 = 4

And either of their sum or difference = b

= - 5

Thus the two terms are - 4 and - 1

Difference = - 4 - 1 = - 5

Product = - 4. - 1 = 4

k^{2} - 4k - k + 4 = 0

k(k - 4) - 1(k - 4) = 0

(k - 4) (k - 1) = 0

k = 4 or k = 1

18