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A Quadratic Equation Whose One Root is 2 and the Sum of Whose Roots is Zero, is - CBSE Class 10 - Mathematics

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Question

A quadratic equation whose one root is 2 and the sum of whose roots is zero, is

  • x2 + 4 = 0

  • x2 − 4 = 0

  •  4x2 − 1 = 0

  • x2 − 2 = 0

Solution

Let `alpha and beta ` be the roots of quadratic equation in such a way that a = 2

Then, according to question sum of the roots

`alpha + beta = 0`

 `2 + beta = 0`

         `beta = -2`

And the product of the roots

`alpha . beta = 2 xx (-2)`

       `= - 4`

As we know that the quadratic equation

`x^2 - (alpha + beta) x + alpha beta = 0`

Putting the value of `alpha and beta` in above

Therefore, the require equation be

`x^2 - 0 xx x + (-4) = 0`

                         `x^2 - 4 = 0`

  Is there an error in this question or solution?

APPEARS IN

Solution A Quadratic Equation Whose One Root is 2 and the Sum of Whose Roots is Zero, is Concept: Solutions of Quadratic Equations by Factorization.
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