Thread: Real zeros of a polynomial function

1. Real zeros of a polynomial function

F(x) = 4x^3 + 7x^2 - 11x - 18
The only one that I could find is -2...from what i have figured out...there is 1 positive real zero and 2 negative real zeros. I have tried everything i cant fins the other...could someone please help

2. Originally Posted by aikenfan
F(x) = 4x^3 + 7x^2 - 11x - 18
The only one that I could find is -2...from what i have figured out...there is 1 positive real zero and 2 negative real zeros.
if you found one to be -2, you can do polynomial long division (or synthetic division) to find $\displaystyle \left( 4x^3 + 7x^2 - 11x - 18 \right) \div (x + 2)$. the result will be a quadratic, and it is easy to find the roots of that

3. For the quadratic, I get 4x^2 - x - 9

4. for the zeros, I get -1.38
as well as 1.63

5. Originally Posted by aikenfan
For the quadratic, I get 4x^2 - x - 9
yes, that is correct. now find the roots of that, there are two real roots

Originally Posted by aikenfan
for the zeros, I get -1.38
as well as 1.63
those seem about right. good job

6. Thank you for the help!