Question

Write the set of values of k for which the quadratic equation has 2x² + kx – 8 = 0 has real roots.

Answer 1

The given quadric equation is 2x² + kx − 8 = 0, and roots are real.

Then find the value of k.

Here, a = 2, b = k and c = -8

As we know that `D =b^2 - 4ac`

Putting the value of  a = 2, b = k and c = -8

` = (k)^2 - 4 xx 2 xx (-8)`

= `k^2 + 64`

The given equation will have real roots, if D > 0

i.e., k² + 64 > 0 which is true for all real values of k

Therefore, for all real values of k, the given equation has real roots.