Answer:
one zero of the quadratic function is x = 6 1/3
Third option is correct.
Step-by-step explanation:
The given quadratic function is [tex]f(x)=9x^2-54x-19[/tex]
For the zeros of this quadratic function, we have f(x)=0
[tex]9x^2-54x-19=0[/tex]
We can write the middle terms as: -54x = 3x-57x
[tex]9x^2+3x-57x-19=0[/tex]
Take GCF as shown below
[tex]3x(3x+1)-19x(3x+1)=0[/tex]
Factored out the common term
[tex](3x+1)(3x-19)=0[/tex]
Apply Zero product property
[tex]3x+1=0,3x-19=0[/tex]
Solve for x
[tex]3x=-\frac{1}{3},\frac{19}{3}[/tex]
We can write 19/3 as 6 1/3.
Hence, one zero of the quadratic function is x = 6 1/3
Third option is correct.
