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- Jul 19th 2006, 11:56 AMLaneSolve these please!!!
questions are on attachment!!!

- Jul 19th 2006, 03:37 PMgalactus
What seems to be the trouble?. Try the Rational Root Theorem.

- Jul 19th 2006, 11:10 PMCaptainBlack
1. Solve $\displaystyle 4x^4+12x^3+x^2-12x+4=0$

First sketch the curve $\displaystyle y=4x^4+12x^3+x^2-12x+4$.

This appears to have a double root at $\displaystyle x=-2$, and it

checks out that $\displaystyle x=-2$ is a root. Then dividing out gives:

$\displaystyle 4x^4+12x^3+x^2-12x+4=(x+2)^2(4x^2-4x+1)$,

from which the remaining roots can be found using the quadratic formula on:

$\displaystyle 4x^2-4x+1=0$.

RonL - Jul 19th 2006, 11:21 PMCaptainBlack
2. Solve $\displaystyle x^3-4x^2-10x+4=0$

Use the same method as I suggested for part 1. Sketch the curve, looks

like a root at $\displaystyle x=-2$ which checks out as a root. So $\displaystyle x-2$ is a

factor of $\displaystyle x^3-4x^2-10x+4$, so divide it out to leave

a quadratic which can then be solved using the quadratic formula.

RonL