Q14 of 50 Page 1

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

Given quadratic equation 9x2 – 3kx + k = 0


Also given the equation has equal roots.


We know that a quadratic equation ax2 + bx + c = 0 has two equal roots, if b2 – 4ac = 0.


Comparing the given equation, we get


a = 9; b = -3k and c = k


⇒ (-3k)2 – 4(9)(k) = 0


⇒ 9k2 – 36k = 0


⇒ 9k (k – 4) = 0


⇒ k = 0 and 4


∴ The values of k are 0 and 4.


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