ACT · Intermediate Algebra · Quadratic equations
Question act-q-00339
Medium Multiple choice No calculator
The question
What is the sum of the solutions to the equation x² − 13x + 42 = 0?
- 42
- 13
- 15
- -13
Show answer & worked solution
Answer: 13
Worked solution. By Vieta's formulas, for x² + bx + c = 0 the sum of the roots is −b. Here −b = 13 = 13. (Or factor: (x − 6)(x − 7) = 0, so the roots are 6 and 7 and their sum is 13.)
Why each wrong choice is wrong. One distractor is the product of the roots (6 × 7). 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 ask you to solve a quadratic, factor a polynomial, or identify the vertex of a parabola.
You will see a question shaped like this one on roughly every other official ACT 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.