If the equation x2 + 2(k + 2)x + 9k = 0 has equal roots then k = ?
Given that the equation x2 + 2(k + 2)x + 9k = 0 has equal roots.
a = 1 b = 2(k + 2) c = 9k
D = b2 - 4ac = 0
(2k + 4)2 - 4.1.9k = 0
4k2 + 16 + 16k - 36k = 0
4k2 - 20k + 16 = 0
k2 - 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
k2 - 4k - k + 4 = 0
k(k - 4) - 1(k - 4) = 0
(k - 4) (k - 1) = 0
k = 4 or k = 1