In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx - 4 = 0
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