I've come across a problem where I know how to do the middle and end of this problem, but I'm a little stuck on the beginning!
I'm told that the x and x2 terms in the expansion of (1 + px +qx2)-2 are 4 and 14 respectively, and I need to find p and q. Obviously I need to get the function into the form [(1 + rx)(1 + sx)]-2 (or similar) to perform the binomial expansion(s). Initially I tried to use the quadratic formula to solve for x in terms of p and q, and from here work out what r and s would be, but this quickly became very unwieldy, and I couldn't successfully simplify the expansion. I feel like I'm missing something really simple in the factorisation of (1 +px +qx2); is there a really simple step I'm missing, or is my method correct?
Thanks very much!