Wave Propagation in Linear Media | re-examined

7.4.1 Zero computation for quadratic arguments
7 Mathematica implementation of a quadrature function
Let f(x) be a quadratic polynomial. We thus need to solve the equation
ax 2 + bx + c =(k+o) ; k 0 (7.3)
for arbitrary coe cients and for the right branch of the parabola. Depending on the coe -
cients, we nd the solutions
x =
8
><
>:
p
,b+ b2 ,4a(c,(k+o) )
2a
,b, p b 2 ,4a(c,(,k+o) )
2a
(k+o) ,c
b
(,k+o) ,c
b
if a>0
if a0
if a =0, b<
>:
d 4ac,b2
4a e if a>0
b 4ac,b2
4a c if a