More than 3000 years ago, the ancient Babylonian mathematicians solved quadratic equatio...

More than 3000 years ago, the ancient Babylonian mathematicians solved quadratic equations. A method they used is demonstrated (using modern notation) in the following example.

To find the positive root of

Rewrite the equation as x(x + 8) = 84, and let y = x + 8. Then the equation to be solved becomes xy = 84. Now take half of the coefficient of x in the original equation, which is 4, and define another variable t by t = x + 4. Then we have x = t − 4 and

y = t + 4. Therefore

With t = 10 we get x = 10 − 4 = 6, the required positive root.

On your own or with a group of classmates, work through the previous example, filling in any missing details if necessary. Then (strictly on your own), use the Babylonian method to find the positive root of each of the following equations. Write out your solutions in detail, as if you were explaining the method to another student who had not seen it before. This will involve a combination of English composition and algebra. Also, in part (b), check your answer by using the quadratic formula.