Solve:

x^3+3x^2-5x-15=0

(a)List all potential zeros

(b)Do synthetic division to solve then finsh

Thanks

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- Dec 5th 2005, 06:05 PMjwaingoldZeros and Synthetic Division
Solve:

x^3+3x^2-5x-15=0

(a)List all potential zeros

(b)Do synthetic division to solve then finsh

Thanks - Dec 5th 2005, 09:32 PMCaptainBlack
Lets look at the very similar equation:

$\displaystyle x^3 + 2.x^2 - 7·x - 14=0$

First thing to do is sketch the graph of:

$\displaystyle x^3 + 2.x^2 - 7·x - 14$

to see if we can find the approximate location of its zeros.

From the sketch in the attachment we see that this has zeros

near -2.7, -2, and +2.7. Trying these out we find that -2 is

an exact root of the cubic. So we may write:

$\displaystyle x^3 + 2.x^2 - 7·x - 14\ =\ (x+2)(A.x^2+B.x+C)$Now you can use synthetic division to find the quadratic, which

in this case turns out to be:

$\displaystyle x^2-7$which may be factorised either by inspection of by using the

quadratic formula to find its roots, and hence its linear factors.

So:

$\displaystyle x^3 + 2.x^2 - 7·x - 14\ =\ (x+2)(x+\sqrt 7)(x-\sqrt 7)$So the solutions of the cubic are $\displaystyle -2,\ -\sqrt 7, +\sqrt 7$.

Your problem can be solved in a similar manner.

RonL