Standard form of polynomial = ax² + bx + c
Zeros: x = {-2,3}
This gives the factors as, (x + 2) (x - 3)
On expanding this:
(x + 2) (x - 3)
x(x - 3) + 2(x - 3)
x² - 3x + 2x - 3
x² - x - 3
Polynomial = <em>x² - x - 3</em>
Answer:
The attendance was 198 children, 90 students and 99 adults.
Step-by-step explanation:
We define:
c: children attendance
s: students attendance
a: adult attendance
The equation that describes the total ticket sales is:
![5c+7s+12a=2808](https://tex.z-dn.net/?f=5c%2B7s%2B12a%3D2808)
We also know that the children attendance doubles the adult attendance:
![c=2a](https://tex.z-dn.net/?f=c%3D2a)
The third equation is the seating capacity, which we assume is full:
![c+s+a=387](https://tex.z-dn.net/?f=c%2Bs%2Ba%3D387)
We start by replacing variables in two of the equations:
![c=2a\\\\s=387-c-a=387-2a-a=387-3a](https://tex.z-dn.net/?f=c%3D2a%5C%5C%5C%5Cs%3D387-c-a%3D387-2a-a%3D387-3a)
Then, we solve the remaining equation for a:
![5c+7s+12a=2808\\\\5(2a)+7(387-3a)+12a=2808\\\\10a+(2709-21a)+12a=2808\\\\10a+12a-21a=2808-2709\\\\a=99](https://tex.z-dn.net/?f=5c%2B7s%2B12a%3D2808%5C%5C%5C%5C5%282a%29%2B7%28387-3a%29%2B12a%3D2808%5C%5C%5C%5C10a%2B%282709-21a%29%2B12a%3D2808%5C%5C%5C%5C10a%2B12a-21a%3D2808-2709%5C%5C%5C%5Ca%3D99)
Then, we solve for the other two equations:
![c=2a=2*99=198\\\\s=387-3a=387-3*99=387-297=90](https://tex.z-dn.net/?f=c%3D2a%3D2%2A99%3D198%5C%5C%5C%5Cs%3D387-3a%3D387-3%2A99%3D387-297%3D90)
The attendance was 198 children, 90 students and 99 adults.
Answer:
12
Step-by-step explanation: