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For what value(s) of k, the roots of the equation \( \Large 9x^{2} + 2Kx + 4 = 0 \) will be equal ?

A) 6
B) -6
C) \( \Large \pm 6 \)
D) \( \Large \pm 5 \)

Correct Answer:



C) \( \Large \pm 6 \)

Description for Correct answer:
Sum of roots = \( \Large 2 \alpha \) = \( \Large \frac{-2k}{9} \)

=> \( \Large \alpha = \frac{-k}{9} \)

Product of roots = \( \Large \alpha^{2} = \frac{4}{9} \)

\( \Large \therefore (\frac{-k}{9})^{2} = \frac{4}{9} \)

=> \( \Large \frac{k^{2}}{81} = \frac{4}{9} => k^{2} = 36 \)

=> \( \Large k = \pm 6 \)

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