f(x) = 2x ^2 - 6xThe total number of seats in an auditorium is modeled by the function f(x), 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? A) 32 B) 13 C) 20 D) 16

The given function is [tex] f(x) = 2x^2 - 6x [/tex]Here [tex] x [/tex] represents the number of rows.[tex] f(x) [/tex] represents the total number of seats in the auditorium.Now the total seats in the auditorium are 416.So [tex] f(x) = 416 [/tex][tex] 2x^2-6x=416 [/tex]Dividing all terms by 2 we get[tex] x^2-3x=208 [/tex]Subtracting 208 from both sides[tex] x^2-3x-208=0 [/tex]Factoring we get(x-16)(x+13)=0Using Zero product rulex - 16= 0 or x+13=0x= 16 or x = -13But as x cannot be negativeSo x = 16There are 16 rows in the auditorium if it has a total of 416 seats.