Find the values of k for equation have real roots4x2 + kx + 3 = 0

1.	Find the values of k for equation have real roots4x2 + kx + 3 = 0
Answer» Given, 4x² + kx + 3 = 0 It’s of the form of ax²+ bx + c = 0 Where, a = 4, b = k, c = 3 For the given quadratic equation to have real roots D = b²– 4ac ≥ 0 D = (k)² – 4(4)(3) ≥ 0 ⇒ k² – 48 ≥ 0 ⇒ k² ≥ 48 ⇒ k ≥ 4√3 and k ≤ -4√3 [After taking square root on both sides] The value of k can be represented as (∞, 4√3] U [-4√3, -∞)

Answer»

Given,

4x² + kx + 3 = 0

It’s of the form of ax²+ bx + c = 0

Where, a = 4, b = k, c = 3

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

D = (k)² – 4(4)(3) ≥ 0

⇒ k² – 48 ≥ 0

⇒ k² ≥ 48

⇒ k ≥ 4√3 and k ≤ -4√3 [After taking square root on both sides]

The value of k can be represented as (∞, 4√3] U [-4√3, -∞)

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