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Question
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
kx2 + 6x - 3k = 0, k ≠ 0
Solution
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.
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