Question

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

पर्याय

• −2

• 2

• \[- \frac{1}{2}\]

• \[\frac{1}{2}\]

Answer 1

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`