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Question
Find the value of k for which the quadratic equation kx (x − 2) + 6 = 0 has two equal roots.
Solution
Given quadratic equation is:
kx( x − 2 )+ 6 = 0
⇒ kx2 − 2kx + 6 = 0
For a quadratic equation to have equal roots,
b2 − 4ac = 0
Comparing the given equation with general equation ax2 + bx + c =0
We get a = k, b = −2k and c = 6
(−2k)2 − 4(k)(6) = 0
⇒ 4k2 − 24k = 0
⇒ 4k ( k − 6 ) = 0
Therefore, k = 0 and k = 6.
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