Determine the set of values of k for the given quadratic equation has

1.	Determine the set of values of k for the given quadratic equation has real roots:kx2 + 6x + 1 = 0
Answer» Given, 2x²+ x + k = 0 It’s of the form of ax²+ bx + c = 0 Where, a = 2, b = 1, c = k For the given quadratic equation to have real roots D = b²– 4ac ≥ 0 D = 1² – 4(2)(k) ≥ 0 ⇒ 1 – 8k ≥ 0 ⇒ k ≤ \(\frac{1}{8}\) The value of k should not exceed \(\frac{1}{8}\) to have real roots.

Determine the set of values of k for the given quadratic equation has real roots:kx2 + 6x + 1 = 0

Answer»

Given,

2x²+ x + k = 0

It’s of the form of ax²+ bx + c = 0

Where, a = 2, b = 1, c = k

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

D = 1² – 4(2)(k) ≥ 0

⇒ 1 – 8k ≥ 0

⇒ k ≤ \(\frac{1}{8}\)

The value of k should not exceed \(\frac{1}{8}\) to have real roots.