solve equations

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July 19th 2006, 11:56 AM
Lane

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Solve these please!!!

questions are on attachment!!!
July 19th 2006, 03:37 PM
galactus

What seems to be the trouble?. Try the Rational Root Theorem.
July 19th 2006, 11:10 PM
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 19th 2006, 11:21 PM
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
a quadratic which can then be solved using the quadratic formula.

RonL

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