Question

The roots of a quadratic equation are 9 and -9. Which of the following quadratic equations has these roots?

A. x^2 + 81 = 0
B. x^2 - 9 = 0
C. x^2 - 81 = 0
D. x^2 + 9 = 0

Answer 1

The correct quadratic equation is x^2 - 81 = 0 (option C).

Step-by-step explanation:

The roots of a quadratic equation are the values of x that make the equation equal to zero. In this case, the roots are 9 and -9.

To find the quadratic equation that has these roots, we can use the fact that the sum of the roots is equal to the opposite of the coefficient of the linear term (b) divided by the coefficient of the quadratic term (a).

For the roots 9 and -9, the sum is 0, so the linear term (b) must be 0. Therefore, the correct quadratic equation is x^2 - 81 = 0 (option C).