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)=2x³+13x²+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)=2x³+13x²+3x-5
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f(x)=2x³+13x²+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"
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