Chapter 6 Projects
QUADRATIC EQUATIONS

RESEARCH PROJECTS Continued Fraction and Golden Ratio

If you successfully completed the research project in Chapter 7, then you used number sequences and inductive reasoning to conclude that the continued fraction

is equal to the golden ratio.

The same conclusion can be found with the quadratic formula by using the following conditional statement

Work with this conditional statement until you see that it is true. Then solve the equation . Write an essay in which you explain in your own words why the conditional statement is true. Then show the details of the solution to the equation . The message that you want to get across in your essay is that the continued fraction shown above is actually the same as the golden ratio.