Accuracy comparison of q1.cpp and q2.cpp.
q2.cpp produces a much better approximation to a root when
the numerator of the usual quadratic formula is near zero.
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Below, q1 and q2 are both asked to find roots of the same polynomial,
whose coefficients are  0.12345e-6 1.0 0.98765e-6.
The answer provided by q2 produces a much smaller value of the
polynomial than that produced by q1.

The relevant data are underlined with "=".
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kiwi.102> q1
For a quadratic polynomial of the form a*x*x + b*x + c,
Enter the real, floating-point coefficients a, b, c: 0.12345e-6 1.0 0.98765e-6
The real roots are: -9.87914e-07, -8.10045e+06
                    ============= 
kiwi.106> eval
For a quadratic polynomial of the form a*x*x + b*x + c,
Enter the real, floating-point coefficients a, b, c: 0.12345e-6 1.0 0.98765e-6
Enter a point at which to evaluate: -9.87914e-07
The value of the polynomial at -9.87914e-07 is -2.64e-10
                                               =========

kiwi.103> q2
For a quadratic polynomial of the form a*x*x + b*x + c,
Enter the real, floating-point coefficients a, b, c: 0.12345e-6 1.0 0.98765e-6
The real roots are: -9.8765e-07, -8.10045e+06
                    ===========
kiwi.107> eval
For a quadratic polynomial of the form a*x*x + b*x + c,
Enter the real, floating-point coefficients a, b, c: 0.12345e-6 1.0 0.98765e-6
Enter a point at which to evaluate: -9.8765e-07
The value of the polynomial at -9.8765e-07 is 1.2049e-19
                                              ==========