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In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root. - Mathematics

Sum

In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.

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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.

Concept: Nature of Roots
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