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

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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

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?
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APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Q: 17 | Page no. 84
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Q: 17 | Page no. 84
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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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