Question

Determine the set of values of k for the given quadratic equation has real roots:

2x² – 5x – k = 0

Answer 1

Given,

2x² – 5x – k = 0

It’s of the form of ax² + bx + c = 0

Where, a = 2, b = -5, c = -k

For the given quadratic equation to have real roots D = b² – 4ac ≥ 0

D = (-5)² – 4(2)(-k) ≥ 0

⇒ 25 + 8k ≥ 0

⇒ k ≥ \(\frac{-25}{8}\)

The value of k should be lesser than \(\frac{-25}{8}\) to have real roots.