# Forming Equations Using Roots

• August 12th 2009, 05:34 AM
xwrathbringerx
Forming Equations Using Roots
Hi

How do I do this question:

The equation 3x^3 + 6x^2 - 4x + 7 = 0 has roots a,b,c. Fnd the equation with roots a + b, a + c, b+ c.

I can do simple ones e.g. roots 1/a, 1/b, 1/c but I failed at this one :(
• August 12th 2009, 06:29 AM
red_dog
Let $x_1=a, \ x_2=b, \ x_3=c$. Then $x_1+x_2+x_3=-2$

$y_1=x_2+x_3=-x_1-2$

$y_2=x_1+x_3=-x_2-2$

$y_3=x_1+x_2=-x_3-2$

Let $y=-x-2\Rightarrow x=-y-2$

Replace x in the equation:

$3(-y-2)^3+6(-y-2)^2-4(-y-2)+7=0\Rightarrow -3y^3-12y^2-8y+15=0$