Need algebra help for Using the rational zeros theorem to find all zeros of a polynomial

Algebra
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Dec 18th, 2015

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First we need to determine what the possible roots/zeros of the equation are. So we will look at p/q where p=factors of -5 and q = factors of 2. So we get these possibilities: 5/1,5/2, -5/1, -5/2, 1/1,1/2,-1/1,-1/2. Now I will choose one to divide into the polynomial using synthetic division.

First I will pick 1/2

1/2 | 2  -3  11  -5

             -1  2   5

______________

       2   -2  10  0

So 1/2 is a root/zero of the polynomial! So we get: 2x^3-3x^2+11x-5 = (x-1/2)(2x^2-2x+10)

Now we can try to solve 2x^2-2x+10. Note if we set this to zero and try to solve it using the quadratic formula, it will give us an irrational answer, meaning it is not a rational root/solution.

x= 2 +- sq root ((-2)^-4(2)(10)) / 2(2)  

x= 2 +- sq root (-76) / 4

When we take the square root of a negative, this gives us a complex solution.


Therefore, the only rational solution is: 1/2

Please let me know if you need any clarification. I'm always happy to answer your questions.
Dec 18th, 2015

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