Question

Identifying the values \(a\), \(b\), and \(c\) is the first step in using the quadratic formula to find solution(s) to a quadratic equation. What are the values \(a\), \(b\), and \(c\) in the following quadratic equation? \(-5x^2 - 9x + 12 = 0\)

- a. \(a = -9, b = 12, c = 0\)
- b. \(a = -5, b = -9, c = 12\)
- c. \(a = 5, b = 9, c = 12\)
- d. \(a = 9, b = 12, c = 0\)

Answer 1

In the quadratic equation -5x² - 9x + 12 = 0, the coefficients are a = -5, b = -9, and c = 12. These values correspond to the variables in the standard form of a quadratic equation, ax² + bx + c = 0, and are used to find the solutions of the equation using the quadratic formula.

Step-by-step explanation:

When solving a quadratic equation of the form ax² + bx + c = 0, the values of a, b, and c are the coefficients of the terms respectively. Looking at the quadratic equation -5x² - 9x + 12 = 0, we identify the coefficients directly:

• a is the coefficient of x², which is -5.
• b is the coefficient of x, which is -9.
• c is the constant term, which is 12.

Therefore, the correct values for the given quadratic equation are a = -5, b = -9, and c = 12, corresponding to option b.