SOLUTION: 4. List all possible (or potential) rational zeros for the polynomial below. Find all real zeros of the polynomial below and factor completely over the real numbers. Please show al

Question 468609: 4. List all possible (or potential) rational zeros for the polynomial below. Find all real zeros of the polynomial below and factor completely over the real numbers. Please show all of your work.
f(x)=2x�+13x�+3x-5

I am no math wiz can you help me please? sincerely.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
4. List all possible (or potential) rational zeros for the polynomial below. Find all real zeros of the polynomial below and factor completely over the real numbers. Please show all of your work.
f(x)=2x�+13x�+3x-5
...
Listing possible rational zeros:
a0=-5: �1 �5
a3= 2: �1 �2
possible rational zeros:
�1, �1/2, �5, �5/2
..
Graphing calculator shows that 1/2 is a factor of f(x)
Divide f(x) by (x-1/2) (by long division or synthetic division)
(2x�+13x�+3x-5)/(x-1/2)=2x^2+14x+10
solving for other two zeros
2x^2+14x+10=0
By quadratic formula:
a=2, b=14, c=10
x=[-14�sqrt(14^2-4*2*10]/2*2
x=[-14�√116]/4
x=-6.19
x=-.807
ans:
zeros: -6.19, -.807, 1/2
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