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Question
Find the values of k for which the roots are real and equal in each of the following equation:
kx(x - 2) + 6 = 0
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Solution
The given equation is
kx(x - 2) + 6 = 0
⇒ kx2 - 2kx + 6 = 0
The given equation is in the form of ax2 + bx + c = 0
where a = k, b = -2k and c = 6
Therefore, the discriminant
D = b2 - 4ac
= (-2k)2 - 4 x (k) x (6)
= 4k2 - 24k
= 4k(k - 6)
∵ Roots of the given equation are real and equal
∴ D = 0
⇒ 4k(k - 6) = 0
⇒ k = 0
Or
⇒ k - 6 = 0
⇒ k = 6
Hence, the value of k = 0, 6.
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