# solve equations

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• Jul 19th 2006, 11:56 AM
Lane
Solve these please!!!
questions are on attachment!!!
• Jul 19th 2006, 03:37 PM
galactus
What seems to be the trouble?. Try the Rational Root Theorem.
• Jul 19th 2006, 11:10 PM
CaptainBlack
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 PM
CaptainBlack
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