Question

In the following determine the set of values of k for which the given quadratic equation has real roots:

2x² + kx - 4 = 0

Answer 1

The given quadric equation is 2x² + kx - 4 = 0, and roots are real.

Then find the value of k.

Here, a = 2, b = k and c = -4

As we know that D = b² - 4ac

Putting the value of a = 2, b = k and c = -4

= k² - 4 x (2) x (-4)

= k² + 32

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

k² + 32

Since left hand side always positive.

So k ∈ R