Question

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

2x² + 3x + k = 0

Answer 1

The given quadric equation is 2x² + 3x + k = 0, and roots are real.

Then find the value of k.

Here, a = 2, b = 3 and c = k

As we know that D = b² - 4ac

Putting the value of a = 2, b = 3 and c = k

= 3² - 4 x (2) x (k)

= 9 - 8k

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

9 - 8k ≥ 0

8k ≤ 9

k ≤ 9/8

Therefore, the value of k ≤ 9/8.