# Algebra - Equations

• Jan 16th 2008, 01:51 PM
weasley74
Algebra - 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 PM
yannick
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 AM
weasley74
Yeah.. I'm still kinda lost..
• Jan 17th 2008, 04:06 AM
earboth
Quote:

Originally Posted by weasley74
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

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```
Now the remaining solutions must be in

\$\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.