Suppose a machine with the floating-point system $\beta = 10$, $t = 8$, $L = -50$, and $U = 50$ is used to calculate the roots of a quadratic equation $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are given real coefficients. For each of the following, state the numerical difficulties that arise when using the standard formula for computing the root. Explain how to overcome these difficulties when possible.
I dont need an answer for all of them, I tried reading the book - I dont understand the concept of $\beta $, $t$, $L$, and $U$, so if you could just explain that in relation to this question, that'd be great. Thank you!