Find the values of k for equation have real rootskx(x – 2) + 6 = 0

1.	Find the values of k for equation have real rootskx(x – 2) + 6 = 0
Answer» Given, kx(x – 2) + 6 = 0 It can be rewritten as, kx² – 2kx + 6 = 0 It’s of the form of ax²+ bx + c = 0 Where, a =k, b = -2k, c = 6 For the given quadratic equation to have real roots D = b²– 4ac ≥ 0 D = (-2k)² – 4(k)(6) ≥ 0 ⇒ 4k² – 24k ≥ 0 ⇒ 4k(k – 6) ≥ 0 ⇒ k ≥ 0 and k ≥ 6 ⇒ k ≥ 6 The value of k should be greater than or equal to 6 to have real roots.

Answer»

Given,

kx(x – 2) + 6 = 0

It can be rewritten as,

kx² – 2kx + 6 = 0

It’s of the form of ax²+ bx + c = 0

Where, a =k, b = -2k, c = 6

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

D = (-2k)² – 4(k)(6) ≥ 0

⇒ 4k² – 24k ≥ 0

⇒ 4k(k – 6) ≥ 0

⇒ k ≥ 0 and k ≥ 6

⇒ k ≥ 6

The value of k should be greater than or equal to 6 to have real roots.

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