#### Question

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

##### Options

−2

2

\[- \frac{1}{2}\]

\[\frac{1}{2}\]

#### Solution

The given quadric equation is x^{2} − x = λ(2x − 1) , and roots are zero.

Then find the value of λ*.*

Here,

`x^2 - x = λ (2x - 1)`

`x^2 - x2λx + λ = 0`

`x^2 - (1 + 2λ)x + λ = 0`

a = 1,b =-(1+2λ) and , c = λ

As we know that `D = b^2 - 4ac`

Putting the value of a = 1,b =-(1+2λ) and , c = λ

`= {-(1 + 2λ)}^2 - 4 xx 1 xx λ`

`=1 + 4λ + 4λ^2 - 4λ`

`= 1 + 4λ^2`

The given equation will have zero roots, if D= 0

`1 +4λ^2 = 0`

`4λ^2 = -1`

`λ^2 = (-1)/4`

`λ = sqrt((-1)/4)`

`= (-1)/2`

Therefore, the value of `λ = -1/2`

Is there an error in this question or solution?

Advertisement

Advertisement

If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ = Concept: Solutions of Quadratic Equations by Factorization.

Advertisement