If the three roots of the polynomial x^3+3x^2-5x+1 are r1,r2,r3, find r1r2+r1r3+r2r3.
Can someone do this step by step so I understand it? I don't really understand how to apply vieta's formula.

Question

If the three roots of the polynomial x^3+3x^2-5x+1 are r1,r2,r3, find r1r2+r1r3+r2r3.
Can someone do this step by step so I understand it? I don't really understand how to apply vieta's formula.

mathmale · Answer

While there may be other ways to solve this problem, mine is pragmatic:  I actually find the roots r1, r2 and r3 (the order in which you name them doesn't matter), and then calculate the sum of products r1*r2 + r1*r3 + r2r3.
Hint:  one root is 1.  This could be named r1:  r1=1.  What are the other two roots?