Free GMAT Practice Problems on Quadratic Equations
with Solutions Sample 3

A set of 10 problems on quadratic equations similar to the GMAT problem solving, with detailed solutions similar to the questions in the GMAT test.

Question 1

Solve the equation x² + 5x = - 6 for x.
A) x = 2 and x = 3
B) x = - 2 only
C) x = - 2 and x = - 3
D) x = - 3 only
E) No solutions

Question 2

Find the values of the constants k and m so that the equation 2 x² + kx - m = 0 has solutions at x = 1 and x = -2.
A) k = 1 and m = - 2
B) k = - 2 and m = - 4
C) k = 2 and m = 0
D) k = 2 and m = 4
E) k = 0 and m = 4

Question 3

Solve the equation (x - 1)(x + 3) = (1 - x) for x.
A) x = 1 and x = - 3
B) x = 1 and x = - 4
C) x = 1 and x = 4
D) x = 1 and x = 0
E) x = 1 and x = 3

Question 4

Solve the equation 2 - (x - 2)² = - 18 for x.
A) x = - 2 + 2 √5 and x = - 2 - 2 √5
B) x = 2 √5 and x = - 2 √5
C) x = 20 and x = -20
D) x = √5 and x = - √5
E) x = 2 + 2 √5 and x = 2 - 2 √5

Question 5

Find a positive value of the constant k so that the equation x² + k x + 4 = 0 has only one solution.
A) 4
B) 3
C) 2
D) 1
E) -2

Question 6

If x = 2 is a solution to the equation (m + 2)x² = 16, where m is a constant, then what is the second solution of this equation?
A) x = 3
B) x = - 3
C) x = - 2
D) x = - 4
E) x = 0

Question 7

If x = - 2 is a solution to the equation (1/2) a x² + 3x - 4 = 0, where a is a constant, then what is the second solution of this equation?
A) x = 4 / 5
B) x = 4
C) x = 5 / 4
D) x = 5
E) There is no second solution

Question 8

Find the values of the constants b and c so the equation x² + bx + c = 0 has solutions at x = 2 and x = -1.
A) b = 2 and c = - 1
B) b = - 2 and c = 1
C) b = 2 and c = 2
D) b = 1 and c = 0
E) b = -1 and c = -2.

Question 9

X and Y are two real numbers such that X + Y = 11 / 5, X · Y = 2 / 5 and X is greater than 1. Find X and Y.
A) X = 1 / 5 and Y = 10
B) X = 2 and Y = 1 / 5
C) X = 2 and Y = 2 / 5
D) X = 3 / 5 and Y = 1 / 5
E) X = 10 and Y = 1 / 5

Question 10

The sum of a number x, such that x is greater than 1, and its reciprocal is equal to 10 / 3. Find x.
A) x = 6
B) x = 1 / 3
C) x = 10
D) x = 3
E) x = 13

Free GMAT Practice Problems on Quadratic Equations with Solutions Sample 3