# Cancellation Round-off Error : Numerical Analysis : Confirmation

I have numerically solved the following quadratic equation:

1.002x2 - 11.01x + 0.01265 = 0.

IS IT POSSIBLE THAT IN THIS INSTANCE EQUATION (2) EQUALS (2A) BELOW:

If b2 - 4ac >0, the quadratic equation ax2 + bx +c = zero has two real solutions x1, x2 given by the typical:

(1) x1 = (-b + sqrt(b^2-4ac))/ (2a) , and

(2) x2 = (-b - sqrt(b^2-4ac))/ (2a)

By rationalizing the numerator it is also given that:

(1a) x1 = -2c / ( b + sqrt(b^2 - 4ac))

(2a) x2 = -2c / ( b - sqrt(b^2 - 4ac))

IS IT POSSIBLE THAT (2) = (2A) ?

Using (2), x1 = (11.01 - 11.0077) / (2 * 1.002) = 0.0012

Using (2a), x2 = (-2 * 0.01265) / (-11.01 -11.0077) = .0012

If (2) done not equal (2a) what is the relative error of (2a) using 4 digit rounding arithmetic.

THANK YOU !!

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1.002x2 - 11.01x + 0.01265 = 0.

IS IT POSSIBLE THAT IN THIS INSTANCE EQUATION (2) EQUALS (2A) BELOW:

If b2 - 4ac >0, the quadratic equation ax2 + bx +c = zero has two real solutions ...

#### Solution Summary

The expert examines cancellations for round-off errors numerical analysis.