#### Question

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

x

^{2}+ 4 = 0x

^{2}− 4 = 04x

^{2}− 1 = 0x

^{2}− 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.