If the sum of the roots of the equation x2 – x = λ (2x – 1) is zero, then λ =
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