SAT · Passport to Advanced Math · Quadratic functions and equations
Question sat-q-00061
Medium Multiple choice No calculator
The question
What is the sum of the solutions to the equation x² + 2x − 3 = 0?
- 2
- -2
- 0
- -3
Show answer & worked solution
Answer: -2
Worked solution. By Vieta's formulas, for x² + bx + c = 0 the sum of the roots is −b. Here −b = -2 = -2. (Or factor: (x − 1)(x − -3) = 0, so the roots are 1 and -3 and their sum is -2.)
Why each wrong choice is wrong. One distractor is the product of the roots (1 × -3). One is the sum with the wrong sign — a Vieta sign-flip slip. One is off by 2.
Test-day tactic. Memorize Vieta: sum of roots is −b/a, product is c/a. You can answer many SAT quadratic questions without ever solving the equation.
About this question type
Items here ask you to solve a quadratic equation by factoring, completing the square, or the quadratic formula; to identify the vertex of a parabola from standard or vertex form; or to interpret the meaning of the vertex, axis of symmetry, or zeros in a real-world context (projectile height, profit, revenue).
You will see a question shaped like this one on roughly every other official SAT form, typically at a moderate position in the section — solidly within the range that separates a 600-band student from a 700-band student. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.