Finding the roots of cubic equations
Hi, I've tried the question below and got stuck halfway =) I'd really appreciate any help!! Thanks!!
QUESTION: ax^3+bx^2+cx+d=0 has roots A, B and C. Find the new equation for roots (A-k), (B-k), (C-k).
From eq given,
Sum of product of roots taking 2 at a time=AB+BC+AC=c/a
Using roots (A-k), (B-k), (C-k),
Sum of product of roots taking 2 at a time
=c/a +(2bk)/a + 3k^2
=-d/a -k(c/a) + (b/a)k^2 - k^3
After this, I got stuck. How do I get the cubic equation? Something just seems wrong. Help! =) Thanks everyone!