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Use the rational zeros theorem to find all the real zeros of the polynomial function....
Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.
`f(x) = x^3 - 2x^2 - 13x - 10`
Find the real zeros of f. Select the correct choice below and, if necessary, fill in the answer box to complete your answer.
b. There are no real zeros
3 Answers | add yours
`f(-1)=0` so that: `x_1=-1`
so that we can write:
So: concerning solutions : `x^2-3x-10` :
`Delta= 9-4(-10)=49 >0` two real solution:
`x=(3+-sqrt(49))/2=(3+-7)/2` `x_2=5` `x_3=-2`
Finally the solution given equation are:
Posted by oldnick on May 1, 2013 at 9:43 PM (Answer #1)
Graphicof cubic show the roots: `x_1=-1;x_2=5;x_3=-2`
Posted by oldnick on May 1, 2013 at 9:49 PM (Answer #2)
High School Teacher
Since `f(x) = x^3-2x^2-13x-10`
we can evaluate the function at all factors of `pm 10` to find possible zeros of the function. In this case, we see that
which means that `x+1` is a factor of `f(x)` . Now use division to get the remaining factors, which gives:
But the quadratic factor will further factor into two linear terms to get
This means that the zeros of the cubic are the negatives of the linear factors to get `x=-1` , `x=-2` and `x=5` .
Posted by lfryerda on May 2, 2013 at 12:40 AM (Answer #3)
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