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 468492: 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
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
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
...
f(x)=2x�+13x�+3x-5
factors of p=5: �1, �5
factors of q=2: �1, �2
Possible rational roots, (p/q): �1, �1/2, �5, �5/2
finding roots by synthetic division:
0).......2.....13.....3......-5
1).......2.....15....18.....13
1/2)...2......14....10.....0 (root=1/2)
f(x)=(x-1/2)(2x^2+14x+10)
2x^2+14x+10=0
x^2+7x+5=0
x=[-7�sqrt(49-4*1*5)]/2
x=(-7�√29)/2
Roots are:1/2, (-7+√29)/2,(-7-√29)/2
I'm not sure what you meant by "factor completely over the real numbers"
RELATED QUESTIONS
4. List all possible (or potential) rational zeros for the polynomial below. Find all... (answered by lwsshak3)

List all possible rational zeros for the polynomial below. Find all real zeros of the... (answered by lwsshak3)

List all of the potential rational zeros of the polynomial function. Do not attempt to... (answered by fractalier)

List all of the potential rational zeros of the polynomial function. Do not attempt to... (answered by solver91311)

For the function f(x) = 3x^4- 4x^3 +x^2+ 6x-2 a. State the degree of the polynomial.... (answered by josgarithmetic)

3x^4-4x^3+x^2+6x-2 a. State the degree of the polynomial. b. State the number of... (answered by josgarithmetic)

1. Use synthetic division to divide the polynomial 2x^3 + 7x^2 � 5 by 3+x and write the... (answered by jim_thompson5910)

list the potential rational zeros of the polynomial function. do not find the zeros.... (answered by vleith)

3x4-4x3+x2+6x-2 This is 3x to the fourth, - 4x to the third, + X to the second, + 6X -2.... (answered by josgarithmetic)