Question 497061: I really need help with this as fast as possible thanks alot!
What are all the possible rational zeros for f(x) = x3 + 8x + 6?
±1, ±6
±1, ±2, ±6
±1, ±2, ±3, ±6
±1, ±2, ±3, ±6, ±12
What are all the possible rational zeros for f(x) = 6x3 + 6x2 – 15x – 2?
±1, ±2, ±1/2, ±1/3, ±2/3, ±1/6
±1, ±2, ±1/3, ±2/3
±1, ±2, ±3
±1, ±2, ±3, ±6
Identify all the rational zeros for f(x) = x3 + 4x2 – 3x – 18.
1, –3, –6
–1, 2, –9
2, –3, –3
–1, –3, 6
Identify all the rational zeros for f(x) = x3 – x2 – 8x + 12.
2, 2, –3
2, –2, 3
–1, 3, 4
1, –3, 4
Identify all the rational zeros for f(x) = x3 + 4x2 – 2x + 15.
1
3
–5
1, 3, –5
How many positive real zeros does the function f(x) = x4 + x3 – 7x – 1 have?
3 or 1
1
2 or 0
0
How many negative real zeros does the function f(x) = x5 + x4 – x2 – x + 1 have?
4, 2, or 0
3
2 or 0
3 or 1
How many imaginary zeros does the function f(x) = 3x4 + 2x3 + 4x + 7 have?
0
2 or 0
4 or 2
4, 2, or 0
Identify the real zeros for the function f(x) = x3 – 3x2 – 53x – 9.
1, –3, –3
–1, 1, 9
Identify the real zeros to the nearest tenth for the function f(x) = x3 – 6x – 9.
3.0
–0.6, 1.4
.8, 2.0
–1.2, .4, 3.0
Identify all zeros for the function f(x) = x3 – 6x2 + 10x – 8.
1, 2, 4
2, 2, 4
4, 1 + i, 1 – i
4, 2 + i, 2 – i
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Re-read the instructions for posting on this site, especially the instruction that says "One question per post." What is NOT going to happen is for someone to do your whole homework assignment, or worse, your test, for you.
Here are a couple of rules to help you though. Rational zeros of a polynomial function, if they exist, must be of the form  where  is an integer factor of the constant term and  is an integer factor of the lead coefficient.
A polynomial function of degree  has exactly zeros, some of which may be complex. Complex zeros ALWAYS show up as conjugate pairs, that is, if  is a zero, then  must also be a zero.
A corollary to the above is that polynomial functions of odd degree must have at least one real zero.
Using the first rule I gave you, you can use either polynomial long division or synthetic division to determine if a potential rational zero is actually a zero of the given polynomial. The quotient of a successful division that identifies a zero can be couched as a lesser degree polynomial funcition. Continue the process until you cannot find any more rational roots or you end up with a quadratic quotient that you can solve with the quadratic formula. In fact, if you get down to a quartic or a cubic, there are general formulas for these too, but you don't have any where you will need to go to those lengths.
If you are a little rusty on your poly long division or synthetic division, check out:
Purple Math Polynomial Long Division
Purple Math Synthetic Division
To determine the number of real zeros use Descartes' Rule of Signs
Purple Math Descartes' Rule of Signs
John
My calculator said it, I believe it, that settles it
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