Q10 of 47 Page 1

Find the values of k for which the quadratic equation 9x2 – 3kx + k = 0 has equal roots.

Given, 9x2 – 3kx + k = 0

For equal roots, the value of discriminant should be zero i.e.,


D = b2 – 4ac = 0


Here, a = 9, b = -3k, c = k


⇒ D = (-3k)2 – 4(9)(k) = 0


⇒ 9k2 – 36k = 0


⇒ k2 – 4k = 0


⸫ k (k – 4) = 0


⸫ k = 0 or k = 4


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