2001 AMC 12 #19 - Polynomial

The polynomial P(x)=x^3+ax^2+bx+c has the property that the average of its zeros, the product of its zeros, and the sum of its coefficients are all equal. The y-intercept of the graph of y=P(x) is 2. What is b?

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[cmysubscriptions]

this is cool

but

this guy should not be a teacher until he can speak like a normal american. i know it's discrimination, but it's a growing problem in american colleges where foreigners are teaching as professors

[planeshaperman]

too easy

[CloudySunrise]

@pureowner138 Wait, there are three zeroes so wouldn't the average of the zeroes be -a/3? Then we would get -a/3=-c=-2, so a=6. Then a+b+c+1=9+b=-2 so b=-11.

[Nihanth93]

dude you're amazing

[NinjaXSong]

hey, do you use "First steps for math olympians?" I'm in 8th grade, and I use the book to learn XD

[Omega231984]

say goodbye to campus classrooms,

[2terence2jones]

i learned something new today.

[Orangeflava]

nice!!