In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + 3x + k = 0
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.