Numerical

Sum

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

(k + 1)x^{2} + (2k + 1)x - 9 = 0, k + 1 ≠ 0.

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#### Solution

The given equation is

(k + 1)x^{2} + (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.

Concept: Nature of Roots

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