SOLUTION: For the following polynomials , find all real and complex roots .(hint: Use the rational root theorem to identify potential roots. 1- y(x) = x^3-1 2- h(x) = x^4 -1 3- g(x) = x

Question 936620: For the following polynomials , find all real and complex roots .(hint: Use the rational root theorem to identify potential roots.
1- y(x) = x^3-1
2- h(x) = x^4 -1
3- g(x) = x^4 +2x^3-16x^2-2x+15
4- f(x) = x^4+ 2x^3 -16x^2 -2x +15
(note:what they mean by potential roots?) .Thanks

Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
to identify POTENTIAL roots use THE RATIONAL ZERO THEOREM
If =+ .... .++ has integer coefficients, then every rational zero of has the following form:

using that, we have:
1-
--> factor and :
= � which is = �
2-
--> factor and :
= � which is = �
3-
--> factor , and :
X ,,,
= �, �,�,�, which is => = �,�,�,�
Test these zeros using synthetic division.
test

|--1-----2----..-16------...-2----15
---| ------1----..-1----..-1------17---..-15
---| 1---- 1----.. -17--------15------- 0
so, is the root
same way you check all other potential roots

now find roots:

1- ........factor: set and use ..(difference of cubes rule)

we already know one root: if =>
use quadratic formula to find other two roots from :

solution will be complex roots:

and

roots:

=>
=>......real roots

=> => => or
.........complex roots

3- ...write as and as
....group

...group

roots:
=>
=>
=>
=> ........all roots are real roots

4- this is same as 3-

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