So here's my problem:
If the equation ax^2 + bx + c = 0 has roots alpha and beta, find the roots of the equation:
ax^2 - bx(x-1) + c(x-1)^2 = 0
What I did:
I managed to simplify the given equation to:
x^2(a-b+c) + x(b - 2c) + c = 0
And now I don't know how to proceed.
A slight push in the right direction would help.
You can also calculate the new roots from the original and by using...
Sum of new roots
Product of new roots
Given that and
you can write and in terms of
then solve for the sum and product of the new roots using .
If you do this, you will find the new roots in terms of the old ones..
the calculations will give
Thank you Henryt999, HallsofIvy, e^(i*pi) & Archie Meade!
I solved the equation using the methods provided by you using
And then used the quadratic equation formula to find the new roots in terms of
The gets canceled, so we're left with only .
The final answer I got is: