ACT · Intermediate Algebra · Quadratic equations
Question act-q-00347
Medium Multiple choice No calculator
The question
What is the sum of the solutions to the equation x² − 5x + 4 = 0?
- -5
- 7
- 4
- 5
Show answer & worked solution
Answer: 5
Worked solution. By Vieta's formulas, for x² + bx + c = 0 the sum of the roots is −b. Here −b = 5 = 5. (Or factor: (x − 4)(x − 1) = 0, so the roots are 4 and 1 and their sum is 5.)
Why each wrong choice is wrong. One distractor is the product of the roots (4 × 1). 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.