SOLUTION: Hey,
I'm not sure how to solve the following - please help:
"using the fact that -2 and 1/3 are zeros of the polynomial (x)=3x^4+5x^3+x^2+5x-2, find the other two zeros."
Algebra ->
Radicals
-> SOLUTION: Hey,
I'm not sure how to solve the following - please help:
"using the fact that -2 and 1/3 are zeros of the polynomial (x)=3x^4+5x^3+x^2+5x-2, find the other two zeros."
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Question 492558: Hey,
I'm not sure how to solve the following - please help:
"using the fact that -2 and 1/3 are zeros of the polynomial (x)=3x^4+5x^3+x^2+5x-2, find the other two zeros."
Thanks! Cramming for huge nasty final whilst caring for a crazy toddler! Answer by Edwin McCravy(20055) (Show Source):
3x4+5x³+x²+5x-2
-2|3 5 1 5 -2
| -6 2 -6 2
3 -1 3 -1 0
So the polynomial has been factored as
(x+2)(3x³-x²+3x-1)
Next you can factor the cubic by grouping:
Factor the first two terms as x²(3x-1) and write the last two
terms as +1(3x-1), and enclose those in brackets:
(x+2)[x²(3x-1)+1(3x-1)]
Factor out (3x-1) leaving x² and +1 in another set of
parentheses:
(x+2)(3x-1)(x²+1)
x+2=0 3x-1=0 x²+1=0
x=-2 3x=1 x²=-1
x= x=±i
The other two zeros are i and -i.
Edwin
