Question

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

Answer 1

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.