Question 1047657: The interval where fx) = -2(x+2)(x-3)(x-1) is positive will be
A) x > 0
B) -2 < x < 1, x > 3
C) x < -2, 1 < x < 3
D) x < 0
Found 3 solutions by MathLover1, solver91311, ikleyn:
Answer by MathLover1(20850)   (Show Source):
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Your function has 3 zeros, -2, 1, and 3. These three values divide the  axis into four regions, less than -2, between -2 and 1, between 1 and 3, and greater than 3.
For each one of these regions, select a value that is NOT one of the zeros. I chose -3, 0, 2, and 4. Take each of these values and substitute into the function. You don't need to calculate the actual value of the function, you just need to determine the sign of each of the factors. Counting the -2 lead coefficient, count the number of negative factors for each one of the selected values. If you have an even number of negative factors, then the value of the function on that interval is positive.
John
My calculator said it, I believe it, that settles it
Answer by ikleyn(52824)  (Show Source):
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