District questions ok now?

[Celsion]

Are district questions allowed to be asked now? If so, I'll post questions when someone replies with an ok.

[MistaPotta]

Sure. The testing windows are over.

~MP

[Celsion]

Thanks. Just two questions, already corrected most on District 1.

36. Points A, B, C, and D are on a circle O such that segment PA is a secant to circle O through point B and segment PC is a secant to circle O through point D. If PB=14", AB=20", PD=10" then CD=?
(a) 37[unparseable or potentially dangerous latex formula]
I used the power of a point theorem and got 47[unparseable or potentially dangerous latex formula] as the answer.

57. Given the function [unparseable or potentially dangerous latex formula] there is a possibility of how many positive real zeroes?
(b) 3 or 1

Anyways, is it me or does the test look so much easier when you go over it slowly?

[MistaPotta]

For 57: Descartes Law of Signs says to find the number of positive real roots, count the number of sign changes in your polynomial. Then, that number is the most possible (minus a multiple of two for possible conjugate complex roots).

Since your polynomial has three sign changes, three is the most possible. Subtracting two for a possible conjugate complex pair of roots, you get 3 or 1.

For 36, I think you found PC. Did you remember to subtract PD=10?

~MP

[Celsion]