I can not seem to grasp this quadratic formula

Question

Select the values of x that are solutions to the inequality 0>x^2 +5x-2

 

A. xΕ(-5-√33⁄2,-5+√33⁄2)

B. xΕ[5-√33⁄2,-5+√33/2]

C. xE(-∞,-5-√33/2)∪(-5+√33/2,∞)

D. xE(-∞,-5-√33/2]∪[-5+√33/2,∞)

Answer 1

Solve 0 > x^2 + 5x -2.

 

Let's think about the graph of y = x^2 + 5x - 2.

 

Since the leading coefficient is positive the parabola opens up.

 

The y-intercept = -2 so the vertex will be below the x-axis and, since the parabola opens up, there will be 2 x-intercepts/zeros.

 

The part of the parabola that is below the x-axis is where y < 0, and that part is between the zeros.

 

So let's find the zeros of y(x) using the quadratic formula:

 

      - b ± sqrt(b^2 - 4ac)    - 5 ± sqrt(5^2 - 4(1)(-2))     - 5 ± sqrt(25 + 8)

x = ------------------------- = ------------------------------- = ----------------------

               2a                                 2(1)                                   2

 

      - 5 ± sqrt(33)
x = ----------------- => answer is A.
                  2

 

(The zeros are not in the interval because y < 0.)