Question

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

3x² + 2x + k = 0

Answer 1

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

Then find the value of k.

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

As we know that D = b² - 4ac

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

= (2)² - 4 x (3) x (k)

= 4 - 12k

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

4 - 12k ≥ 0

12k ≤ 4

k ≤ 4/12

k ≤ 1/3

Therefore, the value of k ≤ 1/3