If x1 and x2 are the roots of the quadratic equation ax2 + bx + c = 0, their product is x1 x2 = c/a. When b is much larger than either a or c, the usual quadratic formula does a poor job of...

If x1 and x2 are the roots of the quadratic equation ax2 + bx + c = 0, their product is

x1 x2 = c/a. When b is much larger than either a or c, the usual quadratic formula

does a poor job of calculating the root with the smaller absolute value because the

numerator is the difference of two nearly equal quantities

and b. Such

subtractions always reduce the number of significant digits in the answer by the

number of leading significant digits that cancel in the subtraction. Write a program

that calculates the roots of a quadratic equation using the quadratic formula, and

then recalculates the smaller root in absolute value using the formula x2 = c/ax1.

Compare the two sets of roots. Test the program on the following equations.