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)X2 + (2k + 1)X - 9 = 0, K + 1 ≠ 0. - Mathematics

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)x2 + (2k + 1)x - 9 = 0, k + 1 ≠ 0.

Solution

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.

Concept: Nature of Roots
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ICSE Class 10 Mathematics