Answer :

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

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