ACT · Elementary Algebra · Polynomial addition and multiplication
Question act-q-00302
Easy Multiple choice No calculator
The question
What is the sum of the solutions to the equation x² − 9x + 20 = 0?
- 9
- 11
- -9
- 20
Show answer & worked solution
Answer: 9
Worked solution. By Vieta's formulas, for x² + bx + c = 0 the sum of the roots is −b. Here −b = 9 = 9. (Or factor: (x − 4)(x − 5) = 0, so the roots are 4 and 5 and their sum is 9.)
Why each wrong choice is wrong. One distractor is the product of the roots (4 × 5). 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 test polynomial arithmetic. The most common surface form is multiplying two binomials (FOIL) or expanding a squared binomial.
You will see a question shaped like this one on roughly every other official ACT form, typically at an early position in the section, where missing them carries an outsize penalty because the curve assumes everyone in your band gets them right. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.
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