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Question
Find the value (s) of k for which each of the following quadratic equation has equal roots : kx2 – 4x – 5 = 0
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Solution
kx2 – 4x – 5 = 0
Here a = k, b = -4, c = 5
∴ D = b2 - 4ac
= (-4)2 - 4 x k x (-5)
= 16 + 20k
∵ Roots are equal.
∴ D = 0
⇒ b2 - 4ac = 0
∴ 16 + 20k = 0
⇒ 20k = -16
⇒ k = `(-16)/(20)`
= `(-4)/(5)`
Hence k = `(-4)/(5)`.
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