Question: One common instance where subtractive cancellation occurs involves finding the roots of a parabola, ax 2 + bx + c, with the quadratic formula: For

One common instance where subtractive cancellation occurs involves finding the roots of a parabola, ax²+ bx + c, with the quadratic formula:

X = -b b - 4ac 2a

For cases where b²>> 4ac, the difference in the numerator can be very small and roundoff errors can occur. In such cases, an alternative formulation can be used to minimize subtractive cancellation:

Use 5-digit arithmetic with chopping to determine the roots of the following equation with both versions of the quadratic formula.

x2 − 5000.002x + 10

X = -b b - 4ac 2a

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