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.

Solve the equation x^{2} + 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

Find the values of the constants k and m so that the equation 2 x^{2} + 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

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

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

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

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

If x =  2 is a solution to the equation (1/2) a x^{2} + 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

Find the values of the constants b and c so the equation x^{2} + 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.

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

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
More Math Practice Tests
Free Practice for GAMT Math tests
Free Compass Math tests Practice
Free Practice for SAT, ACT Math tests
Free GRE Quantitative for Practice
Free AP Calculus Questions (AB and BC) with Answers

