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Question
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
Solution
Given,
kx2 - 6x - 1 =0,
For no real roots, D<0
⇒ b2 - 4ac < 0
⇒ (-6)2 - 4(k)(-1) < 0
⇒ 36 + 4k < 0
⇒ k < -9
For all k < -9, the given quadratic equation does not have any real roots.
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