# For which of the following equations are x = 5 and x = -5 both solutions (a) x^{2 }- 25 (b) x-5 (c) x+5 (d) x^{2}+25

We will use the concept of factorization to find the equation.

## Answer: x^{2 }- 25 is the required equation for which x = 5 and x = -5 both are solution.

Let's see how we use the concept of factorization to find the equation.

**Explanation: **

With the help of the given roots of the equation, we can determine the factors of the polynomial. By multiplying the factors among themselves we will get the required equation.

The roots are given as x = 5 , x = -5 .

Then the factors of the equation can be written as (x - 5) and (x + 5)

On multiplying the factors among themselves we get the required equation

Hence, the required equation will be ( x - 5 ) × ( x +5 )

= x^{2 }- 25