Ron G. answered • 03/21/16
Tutor
4.4
(26)
Multiple levels Math, Science, Writing
OK. The x-intercept, that is where f(x) = 0. We're talking about the "zeros," or "roots." What term gets used pretty much depends on the teacher, even if one of those terms is considered "official." LOL
It's a cubic polynomial. This means you either have three x-intercepts, or just one. If you have just one, that means the other two roots are complex.
Take a look at the formula: 2x^3 - 3x^2 + 2x - 3.
2, 3, 2, 3. Something's repeated there. You have a shortcut to factoring the polynomial. Usually, factoring a cubic polynomial is a lot more work, so... lucky you. LOL
f(x) = 2x^3 - 3x^2 + 2x - 3 = (2x - 3)(x^2 + 1)
The first factor has a root x = 3/2. The second factor has a pair of complex roots. So you have one x-intercept, 3/2.
Always do a sanity check to make sure your answer works. Substitute x = 3/2 into f(x) and you will get 0. You can do a sanity check by hand. But I used Wolfram Alpha. You could even use a tool like Wolfram Alpha to see what the function looks like before you find the roots. That was a good thing for me in this case: it tipped me off to that complex pair of roots, which means (again) only one x-intercept.
Cheers!
