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

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

Transcribed Image Text:

X = -b± √b² - 4ac 2a