Free practice questions/GMAT Focus Edition
GMAT Focus Edition — Algebra: Quadratics & Functions
6 free practice questions with full explanations.
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Start freeQuestion 1
If x^2 - 5x + 6 = 0, what are the values of x?
- A) 2 and 3
- B) -2 and -3
- C) 1 and 6
- D) -1 and -6
Show answer & explanation
Correct answer: A) 2 and 3
Factoring: (x - 2)(x - 3) = 0, so x = 2 or x = 3.
Question 2
If f(x) = 2x^2 - 3x + 1, what is f(2)?
- A) 1
- B) 2
- C) 3
- D) 4
Show answer & explanation
Correct answer: C) 3
f(2) = 2(4) - 3(2) + 1 = 8 - 6 + 1 = 3.
Question 3
What are the roots of x^2 - 9 = 0?
- A) 3 and -3
- B) 9 and -9
- C) 3 only
- D) 0 and 9
Show answer & explanation
Correct answer: A) 3 and -3
x^2 - 9 = (x - 3)(x + 3) = 0, so x = 3 or x = -3.
Question 4
If x^2 + 6x + 9 = 0, what is x?
- A) 3
- B) -3
- C) 9
- D) -9
Show answer & explanation
Correct answer: B) -3
x^2 + 6x + 9 = (x + 3)^2 = 0, so x = -3 is the double root.
Question 5
For f(x) = x^2 - 4x + 7, what is the minimum value of f(x)?
- A) 1
- B) 2
- C) 3
- D) 4
Show answer & explanation
Correct answer: C) 3
The vertex occurs at x = -b/2a = 4/2 = 2. Then f(2) = 4 - 8 + 7 = 3, which is the minimum value since the parabola opens upward.
Question 6
If x^2 - 2x - 15 = 0, what is the sum of the roots?
- A) -2
- B) 0
- C) 2
- D) 5
Show answer & explanation
Correct answer: C) 2
By Vieta's formulas, the sum of the roots equals -b/a = -(-2)/1 = 2. (Factoring confirms: (x-5)(x+3) = 0, roots 5 and -3, sum = 2.)
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