Mathematics
The values of k for which the quadratic equation 9x2 - 3kx + k = 0, has equal roots, are:
0, 1
0, 2
2, 4
0, 4
Quadratic Equations
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Answer
Comparing 9x2 - 3kx + k = 0 with ax2 + bx + c = 0 we get,
a = 9, b = -3k and c = k.
We know that,
Since equations has equal roots,
⇒ D = 0
⇒ b2 - 4ac = 0
⇒ (-3k)2 - 4(9)(k) = 0
⇒ 9k2 - 36k = 0
⇒ 9k(k - 4) = 0
⇒ 9k = 0 or (k - 4) = 0 [Using Zero-product rule]
⇒ k = 0 or k = 4.
Hence, option 4 is the correct option.
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