SOLUTION: Find the sum of the cubes of the roots of {{{ x^2-2x+13=0 }}}, but do not find the roots.

The other tutor did EXACTLY what you were told NOT to do!!!!
She found the roots!!!  She got an approximate version of the
answer, but the answer oames out exactly as an integer.

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Here's how to do it as you were told to do it.

A "monic" polynomial is a polynomial whose leading coefficient is 1.

The coefficient of the next to largest power of x in a monic polynomial is
-1 times the sum of the roots.

The last term of a monic polynomial in x is the product of the roots if the
degree is even [and -1 times the product of the roots if the degree is odd.]

 is a monic polynomial of even degree 2.

Therefore the sum of its roots is 2 and the product of its roots is 13.

Let its roots be  and 

Then  and 






So


Substitute:  and 







Edwin