Concept explainers
Use 5-digit arithmetic with chopping to determine the roots of the following equation with Eqs. (3.12) and (3.13)
Compute percent relative errors for your results.
To calculate: The roots of the equation
Answer to Problem 11P
Solution:
The roots of the equation
And, the roots of the equation
Explanation of Solution
Given:
The equation,
Formula used:
The quadratic formula for the equation
Alternative formula for roots when
Relative error formula:
Calculation:
Consider the following equation,
Here,
Therefore, the roots of the equation from the quadratic formula is,
Thus,
And,
Now, chop to 5 digits and find the root as below,
Solve for two different roots:
And,
Hence, the relative percent error of the first root
And, the relative percent error of the second root
Hence, the roots of the equations are
Now, for the provided equation
Solve for two different roots,
And,
Therefore, the relative percent error of the first root
And, the relative percent error of the second root
Hence, the roots of the equations are
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