Find the value of k for which the given equation has real roots:

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asked Feb 9 in Class X Maths by priya12 (-11,036 points)

Find the value of k for which the given equation has real roots:

(i) kx2 – 6x – 2 = 0

(ii) 9x2 + 3kx + 4 = 0

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1 Answer

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answered Feb 9 by muskan15 (-1,926 points)

(i) The given equation is :

kx2 – 6x – 2 = 0

Here, a = k, b = - 6 &  c  =  - 2

This equation has real root if

b2 – 4ac  ≥ 0

⇒ (- 6)2 – 4 × k × (- 2) ≥ 0

⇒ 36 + 8k ≥ 0

⇒ 8k  ≥ - 36

⇒  k ≥  - 36/8  ⇒ k ≥ - 9/2

(ii) The given quadratic equation is :

9x2 + 3kx + 4 = 0

Here, a = 9, b = 3k and c = 4

This  equation has real roots if

b2 – 4ac ≥ 0

⇒ (3k)2 – 4 × 9 × 4 ≥ 0

⇒ 9k2 – 144 ≥ 0

⇒ 9k2  ≥ 144

⇒  k2  ≥  144/9  ⇒ k ≥ 12/3

⇒  k ≥ 4.

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