Question

The roots of the quadratic equation \( ax^2 - bx - c = 0 \) are:

• A. \( \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)
• B. \( \frac{b \pm \sqrt{b^2 + 4ac}}{2a} \)
• C. \( \frac{-b \pm \sqrt{b^2 + 4ac}}{2a} \)
• D. \( \frac{b \pm \sqrt{b^2 - 4ac}}{2a} \)

Hint:

The quadratic formula for the roots of \( ax^2 + bx + c = 0 \) is \( \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

Answer 1

The Correct Option is A

The general formula for the roots of the quadratic equation \( ax^2 + bx + c = 0 \) is derived from the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. \] For the equation \( ax^2 - bx - c = 0 \), the formula remains the same. Therefore, the roots of this equation are given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. \] Thus, the correct answer is \( \boxed{\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}} \).