Exercise 2.

Find the roots of the polynomial tex2html_wrap_inline62 by completing the square.

Answer.

First, we want to find the two solutions of the equation

displaymath64

Divide by the leading term 2:

displaymath65

Transfer the constant term to the other side:

displaymath66

We complete the square by adding 25/16 on both sides, since we will exploit the binomial formula

displaymath67

Our equation now reads as:

displaymath68

Simplify:

displaymath69

Take square roots:

displaymath70

and solve for x:

displaymath71

Our two roots are

displaymath72

Consequently the polynomial can be factored as

2displaymath73

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Helmut Knaust
Sat Jun 21 21:01:03 MDT 1997

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