I need help solving these equations;

6x^3+17x^2-3x-20=0

And

X^4-4x^3-7x^2+22x+24=0

Thank you

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- Jan 16th 2008, 01:51 PMweasley74Algebra - Equations
I need help solving these equations;

6x^3+17x^2-3x-20=0

And

X^4-4x^3-7x^2+22x+24=0

Thank you - Jan 16th 2008, 05:44 PMyannick
In both cases u should have a look to the rational root theorem.

With it u can find rational roots and then divide the polynomial till u get to an equation that u know how to solve - Jan 17th 2008, 12:59 AMweasley74
Yeah.. I'm still kinda lost..

- Jan 17th 2008, 04:06 AMearboth
Hello,

as yannick has suggested try to find a rational solution for the first equation.

By trial and error you'll see that x = 1 is a solution. Thus (x -1) can be factored out of the LHS term of the equation. Use long division:Code:`(6x^3 + 17x^2 - 3x - 20) ÷ (x - 1) = 6x^2 + 23x + 20`

-(6x^3- 6x^2)

---------------

23x^2 - 3x

-(23x^2 - 23x)

---------------

20x - 20

-(20x - 20)

------------

0

$\displaystyle 6x^2 + 23x + 20 = 0$

With the 2nd equation start with x = -1. Use long division. Try to get another rational solution, use long division again until you have a quadratic equation which can be solved algebraically.