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Question
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 4kx + k = 0
Solution
The given equation is x2 - 4kx + k = 0
The given equation is in the form of ax2 + bx + c = 0
where a = 1, b = -4k and c = k
Therefore, the discriminant
D = b2 - 4ac
= (-4k)2 - 4 x (1) x (k)
= 16k2 - 4k
∵ Roots of the given equation are real and equal
∴ D = 0
⇒ 16k2 - 4k = 0
⇒ 4k(4k - 1) = 0
⇒ 4k = 0
⇒ k = 0
Or
⇒ 4k - 1 = 0
⇒ 4k = 1
⇒ k = 1/4
Hence, the value of k = 0, 1/4
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