Question

For a quadratic equation, the sum of the roots is -7, and the sum of the squares of the roots is equal to 25. What is the equation?

A. (x² + 7x + 12 = 0)
B. (x² + 7x - 12 = 0)
C. (x² - 7x + 12 = 0)
D. (x² - 7x - 12 = 0)

Answer 1

To find the quadratic equation, assume the equation is ax² + bx + c = 0. By solving two simultaneous equations derived from the given information, we find that the correct quadratic equation is x² + 7x + 12 = 0.

Step-by-step explanation:

To find the quadratic equation, let's assume the equation is ax² + bx + c = 0.

According to the given information, the sum of the roots, which represents the sum of the solutions for x, is -7. This means that the sum of the roots can be expressed as (-b)/a. So, (-b)/a = -7.

Also, the sum of the squares of the roots is equal to 25, which can be expressed as (c/a) = 25.

Now, solving these two equations simultaneously will give us the values of a, b, and c, allowing us to determine the quadratic equation.

By substituting the values of a = 1, b = 7, and c = 12 into the equation ax² + bx + c = 0, we can see that the correct quadratic equation is x² + 7x + 12 = 0.