Question

find the values of k for which the following equation has equal roots :-

(k-12)x^2 + 2 (k-12)x + 2 = 0

Answer 1

(k - 12)x² + 2(k - 12)x + 2 = 0
a = k - 12
b = 2(k - 12) = 2k - 24
c = 2

To have equal roots, the discriminant must equal to 0
D = 0
b² - 4ac = 0
(2k - 24)² - 4 . (k - 12) . 2 = 0
4k² - 96k + 576 - 8k + 96 = 0
4k² - 104k + 672 = 0 (divide by 4 for both sides of equation)
k² - 26k + 168 = 0
k² - 12k - 14k + 168 = 0
k(k - 12) - 14(k - 12) = 0
(k - 12)(k - 14) = 0
k = 12 (not acceptable) or k = 14 (acceptable)

Answer 2

Answer:

K =12 and k =14.I

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