# solve equations

• July 19th 2006, 12:56 PM
Lane
questions are on attachment!!!
• July 19th 2006, 04:37 PM
galactus
What seems to be the trouble?. Try the Rational Root Theorem.
• July 20th 2006, 12:10 AM
CaptainBlack
1. Solve $4x^4+12x^3+x^2-12x+4=0$

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

This appears to have a double root at $x=-2$, and it
checks out that $x=-2$ is a root. Then dividing out gives:

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

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

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

RonL
• July 20th 2006, 12:21 AM
CaptainBlack
2. Solve $x^3-4x^2-10x+4=0$

Use the same method as I suggested for part 1. Sketch the curve, looks
like a root at $x=-2$ which checks out as a root. So $x-2$ is a
factor of $x^3-4x^2-10x+4$, so divide it out to leave