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Question
If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ =
Options
−2
2
\[- \frac{1}{2}\]
\[\frac{1}{2}\]
Solution
Equation is x2 − x = λ (2x − 1)
x2 – x – λ (2x – 1) = 0
x2 – (2λ + 1)x + λ = 0
Here a = 1, b = – (2λ + 1), c = λ
Sum of the roots = `– b/a`
⇒ – (– (2λ + 1)) = 0
⇒ λ = `– 1/2`
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