How would you solve x^3-3x^2+2=0?



Given P(x)=x^3-2x^2-x+8 how could you use its graph to solve x^3-2x^2>4x-8? Does it show you where it shifts and to what quadrant? I'm confused. What is the solution to x^3-2x^2>4x-8?


Thank you.

Solving x^3-3x+2=0, you can try and factor it, or you can use Newton's method. Let's go the factoring route first:
(x+a)(x+b)(x+c) = x^3 + (ab+ac+bc)x^2 + (a+b+c)x + abc
From your equation, abc=2, a+b+c=0 Any ideas? I've got one, a=b=-1, c=2. Does that give you the correct coefficient for x^2? Yup. Okay, so that's how I'd solve that equation.

Second part of your post, given P(x) = x^3-2x^2-4x+8, (note the bold. I'm assuming you made a typo), how could you use the graph to solve inequality (.. . )?

Well, let Q(x) = x^3-2x^2, R(x) = 4x-8.

P(x) = Q(x) - R(x), right?

Your inequality is

Q(x) > R(x), but if we move all of the terms over to the left side:
Q(x) - R(x) > 0, hey, we can re-write this!
P(x) > 0

So, if you can plot P(x), the solution to the inequality will be all values of x for which P(x) > 0.

If you want to figure out what the solution to the inequality is, factor P(x) to find out where the zeros of the equation are, then just perform a test of a number between each of the zeros, and above the highest & below the lowest.