For the floating point system $(B, t, L, U) = (10,8,-50,50)$ and for the quadratic equation:
$ax^2 + bx + c$, I need to show error that arises in various cases and how to fix those.
$$a=10^{-30}$$ $$b= -10^{30}$$ $$c=10^{30}$$
I think there is cancellation error when plugging into quadratic formula. Can anyone help me verify that if multiply quadratic formula by conjugate, then I'll get $\frac{2c}{-b \pm \sqrt{b^2-4ac}}$ which will take away the error for the case that is subject to error?
Thanks!