For which of the following equations are x = 5 and x = –5 both solutions?,
(a).x² + 25
(b).x² - 10
(c).x² - 25
(d).x² + 10

We will use the concept of a quadratic equation to find the required equation.

Answer: Here x = 5, and x = -5 are both solutions of the equation (c) x²-25

Let us understand the solution with the help of the following explanation.

Explanation:

The given two solutions are x = 5, and x = -5.

This can be written as x - 5 = 0, and x + 5 = 0.

Further combining these two we have (x - 5)(x + 5) = 0.

Finally we have (x - 5)(x + 5) = x² - 25.

Hence, for the solutions x = 5 and x = –5, we have the equation x² - 25.