Question

How does one solve a polynomial absolute value inequality? say,
|(x-a)(x-b)(x-c)|>d

Answer 1

No joke, I got a prob on a quiz for my AP BC calc class and I miserably got it wrong...

Answer 2

the lesson mentioned inequalities for polynomials, but not polynomial abs value probs.

Answer 3

And, if I'm supposed to use a graphing calculator, tell me, because I honestly have no idea.

Answer 4

I think these are tricky.
I would re-write as
(x-a)(x-b)(x-c) - d > 0
or
-(x-a)(x-b)(x-c) - d > 0
multiply out and then factor to find the zeros
then look for intervals where the product of the factors are positive
very messy...

Answer 5

Yes, but linear absolute value problems can have extraneous solutions...

Answer 6

then check the possible answers in the original equation

Answer 7

So I probs just want a graphing calculator?

Answer 8

off hand, I don't know. do you have a specific example?

Answer 9

Let me access my course. Sec

Answer 10

|x^3-x^2+x-1|<3
"Round your answer to three decimal places and place in ascending order with a comma in between."
Answer: -0.811<x<-0.732 Incorrect Response
(-.811, 1.743, -.811,1.743, -0.811,1.743, -0.811, 1.743)

Answer 11

yeah, and my answer was from wolfram. I have no idea what I was supposed to do. and the lesson was not helpful at all. Didn't even mention it.

Answer 12

I'll think about it, as this is not something I've looked at very carefully.
But I not that x=1 gives 0 so 1 is part of the solution space.
Maybe by tomorrow I'll have something to post.

Answer 13

Alright. Thanks for looking at it with me.

Answer 14

if you graph the inner polynomial, whenever it goes negative, it just mirrors above the x axis

Answer 15

well, the curve does, then pick a point that is clearly not on the curve to test