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In the Problem 5 of Homework #1, for the given coefficients a= 1,b=−1e5 and c= 1,...

In the Problem 5 of Homework #1, for the given coefficients a= 1,b=−1e5 and c= 1, the root formula gives two real roots

r1= (−b−√∆)/(2a) = 1.0000003385357559e−05,

r2= (−b+√∆)/(2a) = 9.9999999989999997e+ 04

If we plug these two roots back into the quadratic function, we obtain

f(r1) =−3.3844e−07,

f(r2) = 0

We see that root r1 is not correct up to the round-off error.

(a) Explain what the problem is with the formula for evaluatingr1numerically?

(b) Come up with a way to fix it. Modify your code and recalculate the roots for a= 1,b=−1e5 and c= 1.

Check your result by plugging the root back to the quadratic polynomial.

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