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I can not seem to grasp this quadratic formula

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,∞)
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1 Answer

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


Thank you so much Steve!!!! I am Christine from Indianapolis math  partner and you have really helped us both to understand this formula. I think we were intimidated with the different symbols and could not focus  on the formula. The way you explained it made perfect sense and we were able to come up with the same answer as you!!!!! You are great!!!!!