Question

The total number of seats in an auditorium is modeled by f(x)=2x^2−6x
, where x
represents the number of rows of seats. How many rows are there in the auditorium if it has a total of 416 seats?

(1 point)
Responses

16
16

13
13

20
20

32
32

Answer 1

Solve 2x^2 − 6x = 416:
2x^2 − 6x − 416 = 0 → x^2 − 3x − 208 = 0.
Discriminant = 9 + 832 = 841 → √841 = 29.
x = (3 ± 29)/2 → x = 16 or x = −13. Number of rows must be positive, so x = 16.