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(x-1)(x+4)<0 | Change < to = and find the zeroes by solving for x (each factor).
x=1, x=-4 |Set up and test intervals based on those zeroes: x < -4, -4 < x < 1, x > 1
x < -4, choose -4: (-5-1)(-5+4) = -6*-1 = 6 which is not < 0. This interval doesn't work.
-4 < x < 1, choose 0: (0-1)(0+4) = -1*4 = -4 < 0. This interval works.
x >1, choose 2: (2-1)(2+4) = 1*6 = 6 not < 0. This interval doesn't work.
The answer is -4 < x < 1.
If you know parabolas, or graph this, you will see this is less than 0 between the zeroes. Check out the graph (at the bottom).
|Solved by pluggable solver: SOLVE quadratic equation with variable|
|Quadratic equation (in our case ) has the following solutons:|
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant : .
Discriminant d=25 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 1, -4.
Here's your graph:
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