Exercise 1.

Find the roots of the polynomial tex2html_wrap_inline24 by completing the square.

Answer.

We want to find the two solutions of the equation

displaymath26

Transfer the constant term to the other side:

displaymath27

We complete the square by adding 25 on both sides (using the binomial formula tex2html_wrap_inline38 ):

displaymath28

Simplify:

displaymath29

Take square roots:

displaymath30

and solve for x:

displaymath31

Our two roots are tex2html_wrap_inline42 , and tex2html_wrap_inline44 .

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