Which is a zero of the quadratic function f(x)=9x^2-54x-19? a. x=1/3 b. x=3 1/3 c. x= 6 1/3 d. x= 9 1/3 someone

A zero, or a solution of the quadratic function is c) x = 6 1/3

Write -54x as a difference
9x^2 + 3x - 57x - 19

Factor 3x out
{ 9x^2 + 3x }  - 57x - 19
3x (3x + 1)

Factor -19 out
3x (3x + 1) -19 (3x + 1)

Group the equations
( 3x - 19 ) ( 3x + 1 )

Solve for the zeroes

(3x+1) = 0
     -1     -1
3x = -1
3x / 3 = x
-1 / 3 = -1/3
x = - 1/3

(3x - 19) = 0
      +19   +19
3x = 19
3x / 3 = x
19 / 3 = 6 1/3
x = 6   1/3