Loading [MathJax]/jax/output/HTML-CSS/jax.js
Home / Aptitude Tests / Mathematics / Solve the following ...
Solve the following quadratic inequality: x2x -...

Solve the following quadratic inequality: x2x - 4 ≤ 2

A.

3<x<2

B.

2x3

C.

x2,x3

D.

2<x<3

Correct answer is B

x2x42
Subtract two from both sides to rewrite it in the quadratic standard form:
= x2x4222
= x2x60
Now set it = 0 and factor and solve like normal.
= x2x - 6=0
= (x3)(x+2)=0
x + 2 = 0 or x - 3 = 0
x = -2 or x = 3
So the two zeros are -2 and 3, and will mark the boundaries of our answer interval. To find out if the interval is between -2 and 3, or on either side, we simply take a test point between -2 and 3 (for instance, x = 0) and evaluate the original inequality.
= x2x42
= (0)2(0)42
= 0042
42
Since the above is a true statement, we know that the solution interval is between -2 and 3, the same region where we picked our test point. Since the original inequality was less than or equal, we include the endpoints.
2x3.