# Thread: Finding an Equation of a Polynomial

1. ## Finding an Equation of a Polynomial

The roots of the equation 6x^3+17x^2-5x-6=0 is represented by a,b, and c (from least to greatest). Determine an equation whose roots are a+b, a/b, and ab.
I got the roots of the first equation, which are x+3, 2x+1, and 3x-2, but I don't get how to do the second part. I think you list three cubic equations and solve for a,b, and c, but what do you do with d?

Thanks!

2. ## Re: Finding an Equation of a Polynomial

Originally Posted by Dragon08
The roots of the equation 6x^3+17x^2-5x-6=0 is represented by a,b, and c (from least to greatest). Determine an equation whose roots are a+b, a/b, and ab.
I got the roots of the first equation, which are x+3, 2x+1, and 3x-2, but I don't get how to do the second part. I think you list three cubic equations and solve for a,b, and c, but what do you do with d?

Thanks!
x+3, 2x+1, and 3x-2 are not the roots, they're factors of the polynomial. (x+3)(2x+1)(3x-2) = 6x^3+17x^2-5x-6

Get the roots by setting each of these factors equal to zero: x+3=0, 2x+1=0, and 3x-2=0. Solve each for x.

3. ## Re: Finding an Equation of a Polynomial

(From my post at MMF)
x + 3 is a FACTOR; the corresponding root is x = -3
2x + 1 is a factor <=> x = -1/2 is a root
3x - 2 is a factor <=> x = 2/3 is a root.

And there we have them... a, b, and c.
a + b = -3 + -1/2 = -7/2
For this to be a root, (2x + 7) will be a factor.
Then for a/b = 6 to be a root, (x - 6) will be a factor.
Likewise for ab.

Then multiply the factors together!

http://www.mymathforum.com/viewtopic...t=24007#p95919