Question

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.

Answer 1

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.