Tuesday

October 21, 2014

October 21, 2014

Posted by **Allie** on Monday, October 25, 2010 at 10:30pm.

4x^(3)-17x^(2)+16=0

- math -
**MathMate**, Tuesday, October 26, 2010 at 10:06amBy the Descartes rule of signs, we know that there are two positive roots out of three, which also tells us that all the roots are real.

Using the rational zero theorem, we know that rational roots, if any, have to be of the form ±p/q, where p is a factor of 16, and q is a factor of 4.

So the possible rational zeroes are:

±(1/4,1/2,1,2,4,8 and 16), from which we can find x=4 is a root.

Use polynomial division to reduce the polynomial to a quadratic from which the two remaining (irrational) roots can be found.

Note: If we differentiate the polynomial and equate to zero, we find that the local maximum/minimum are at 0 and 2.8. The theorem on bounds tells us that there is a zero between 0 and 2.8, and the other two are at <0 and >2.8 respectively.

**Answer this Question**

**Related Questions**

colag - use the rational zero theorem and descartes’ rule of signs to assist you...

math - I HAVE THESE ANSWERS FOR THE PROBLEMS. COULD YOU DOUBLE CHECK PLEASE, ...

math - Could you please solve so I can double check my answers for the practice ...

college algebra - Use the theorem on bounds to establish the best integral ...

college algebra - Use the theorem on bounds to establish the best integral ...

college algebra - Use the theorem on bounds to establish the best integral ...

college algebra - Use the theorem on bounds to establish the best integral ...

ALGEBRA 2 - Use the Rational Root Theorem to list all possible rational roots ...

pre-calculus - List the possible rational roots of each equation. Then determine...

Algebra HELP! - Do not solve, show possibilities of Descartes's rule of signs ...