# How do you solve # x^2>3x + 4#?

##### 2 Answers

#### Explanation:

**First, transfer everything to one side.**

**Next, factor the quadratic equation.**

**Finally, we will create a table of signs.** We will use the critical points 4 and -1 (taken from step 3).

Critical Points: -1, 4

**Since we want the product to be greater than 0, we will choose the intervals where the product is positive (+).**

The solution set is the interval:

Solve x^2 > 3x + 4.

Ans: (-infinity, - 1) and (4, infinity)

#### Explanation:

Write the quadratic inequality in standard form: f(x) = x^2 - 3x - 4 > 0

First, solve y = 0 to find the 2 x-intercepts (real roots).

Factor pairs of (4) --> (-1, 4). This sum is 3 = -b. Then, the 2 real roots are: -1 and 3.

The parabola opens upward (a > 0). Between the two x-intercepts, f(x) is negative. f(x) > 0 outside the interval (-1, 4)

Answer. Open intervals: (-infinity, -1) and (4, infinity).

graph{x^2 - 3x - 4 [-10, 10, -5, 5]}

NOTE. The method that discusses the signs of the 2 binomials is unadvised because it is complicated and easily leads to errors/mistakes.