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The equation x^2+kx+9=0 has equal roots for Single correct option
The equation
x 2 + k x + 9 = 0 x^2+kx+9=0 x 2 + k x + 9 = 0 has equal roots for
A. k = 6 k=6 k = 6 B. k = ± 3 k=\pm3 k = ± 3 C. k = ± 6 k=\pm6 k = ± 6 D. k = 9 k=9 k = 9 Show answer and solution Answer: (C) k = ± 6 k=\pm6 k = ± 6
Equal roots need discriminant zero:
k 2 − 4 ⋅ 1 ⋅ 9 = 0 k^2-4\cdot1\cdot9=0 k 2 − 4 ⋅ 1 ⋅ 9 = 0 , so
k 2 = 36 k^2=36 k 2 = 36 and
k = ± 6 k=\pm6 k = ± 6 . Both signs work because
k k k enters the discriminant squared; choosing only
+ 6 +6 + 6 is the usual trap.
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