Question

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

2x² + kx + 2 = 0

Answer 1

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

Then find the value of k.

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

As we know that D = b² - 4ac

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

= k² - 4 x (2) x (2)

= k² - 16

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

⇒ k² - 16 ≥ 0

⇒ k² ≥ 16

`rArrk>=sqrt16`Or `k <=-sqrt16`

⇒ k ≥ 4 Or k ≤ -4