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# If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ = - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### Question

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

•  −2

• 2

• $- \frac{1}{2}$

• $\frac{1}{2}$

#### Solution

The given quadric equation is x2 − 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?

#### APPEARS IN

Solution 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.
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