Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:

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asked Feb 16 in Class X Maths by navnit40 (-2,750 points)

Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:

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answered Feb 16 by priya12 (-11,279 points)

(i) The given quadratic equation is

Kx2 + 6x – 3k = 0

Here, a = k, b = 6  and c = - 3k

Sum of the roots  α + β = -b/a = - 6/k

And product of the roots αβ  = c/a = -3k/k

Since, Sum of the roots = product of the roots

 ⇒  - 6/k = -3

⇒ k  =  + 6/+ 3  ⇒ k = 2

(ii) The given equation is

(k + 1)x2 + (2k + 1)x – 9 = 0

Here,  a = k + 1, b = (2k + 1) and c = - 9

Sum of the roots  α + β = -(2k + 1)/k + 1

and   αβ  = c/a =  - 9/k + 1

Since, sum of the roots = Product of the roots

Then, (2k + 1/k + 1) = 9/k + 1

⇒  2k + 1 = 9

⇒ 2k = 9 – 1

⇒ 2k = 8

⇒ k = 8/2 = 4

⇒ k = 4

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