SAT Math: Find the Sum and Product of the Roots of 5x² - 15x - 7 = 0 (Vieta's Formulas)

Exact Question Text

What is the sum of the solutions to the quadratic equation 5x^2 - 15x - 7 = 0?

1. Step-by-Step Formal Solution

1. In ax^2 + bx + c = 0, sum of roots = -b/a.
2. a = 5, b = -15 => -(-15)/5 = 15/5 = 3.

2. Fast Desmos / Calculator Shortcut

Type solutions in Desmos using quadratic formula and add them: sum equals exactly 3.

3. Distractor Trap Analysis

• Trap A (Sign Flip): Forgetting to reverse inequality or dropping negative sign.
• Trap B (Partial Evaluation): Solving for intermediate variable and stopping early.
• Trap C (Extreme Assumption): Over-inferring beyond textual evidence.
• Option Correct: Accurately satisfies all algebraic and logical constraints.