# Math III Honors 2nd period

### 4.6 problems #29 & #31

"Your friend is using Descartes's Rule of Signs to find the number of negative real roots of x^3 + x^2 + x + 1 = 0. Describe and correct the error."

I've worked out problem 29 above. The error in the problem has been identified in the boxed in area. This is the error because in order to find the negative real roots every variable has to be changed into a negative. Under the "should be..." Section I have worked out how the signs would change.

The first sign would be negative because three negatives multiplied together would still be negative.

The second sign is positive because two negatives multiplied together is a positive.

The third sign is negative because it's a positive (+ sign in front) times a negative which equals a negative.

So the equation that is circled and written at the bottom is the correct way.

This is number 31.

This a brace map to show the breakdown of the word problem above.

This picture is of the work I did to get to an equation with "y=" in order to use the graphing calculator to find the value of "h"; which is the height.