Question 86808: I do not understand quadratic equations. Here's my question from my book. Solve each equation and inequality. Write the solution set for each inequality in interval notation.
a.) x^2 - x - 12 = 0
b.) x^2 - x - 12 < 0
c.)x^2 - x - 12 > 0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Write the solution set for each inequality in interval notation.
a.) x^2 - x - 12 = 0
(x-4)(x+3)=0
x=4 or x=-3
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b.) x^2 - x - 12 < 0
(x-4)(x+3) < 0
This product will be <0 where the signs are different.
Draw a number line and plot x=-3 and +4 on it.
Test each of the three intervals of the line to see where the solution set interval(s) is(are).
If x--10 you get (-)(-) so no solutions in (-inf,-4)
If x=0 you get (-)(+) so solutions in (-4,3)
If x=+10 you get (+)(+) so no solutions in (3,+inf)
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c.)x^2 - x - 12 > 0
(x-4)(x+3) >0
From the work done above you see there are solutions in
(-inf,-4) and in (3,+inf)
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Cheers,
Stan H.
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