Find the values of k for equation have real rootsx2 – 4kx + k = 0

1.	Find the values of k for equation have real rootsx2 – 4kx + k = 0
Answer» Given, x² – 4kx + k = 0 It’s of the form of ax²+ bx + c = 0 Where, a =1, b = -4k, c = k For the given quadratic equation to have real roots D = b²– 4ac ≥ 0 D = (-4k)² – 4(1)(k) ≥ 0 ⇒ 16k² – 4k ≥ 0 ⇒ 4k(4k – 1) ≥ 0 ⇒ k ≥ 0 and k ≥ \(\frac{1}{4}\) ⇒ k ≥ \(\frac{1}{4}\) The value of k should be greater than or equal to \(\frac{1}{4}\)to have real roots.

Answer»

Given,

x² – 4kx + k = 0

It’s of the form of ax²+ bx + c = 0

Where, a =1, b = -4k, c = k

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

D = (-4k)² – 4(1)(k) ≥ 0

⇒ 16k² – 4k ≥ 0

⇒ 4k(4k – 1) ≥ 0

⇒ k ≥ 0 and k ≥ \(\frac{1}{4}\)

⇒ k ≥ \(\frac{1}{4}\)

The value of k should be greater than or equal to \(\frac{1}{4}\)to have real roots.

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