Respuesta :
Let us find Zeros of our equation by equating our quadratic function to zero.
[tex]9x^{2}-54x-19=0[/tex]
We will factor out our quadratic function by splitting the middle term.
[tex]9x^{2}-57x+3x-19=0[/tex]
Now we will factor out GCF from both groups. We can see that GCF of our first group is 3 and GCF of second group is 1.
[tex]3x(3x-19)+1(3x-19)=0[/tex]
After factoring out the common binomial we will get,
[tex](3x-19)(3x+1)=0[/tex]
Now we will equate each binomial to zero to find both zeros of our quadratic function.
[tex]3x-19=0 \text{ or }3x+1=0[/tex]
[tex]3x=19 \text{ or } 3x=-1[/tex]
[tex]x=\frac{19}{3}=6\frac{1}{3}\text{ or } x=\frac{-1}{3}[/tex]
Therefore, [tex]x=6\frac{1}{3}[/tex] and [tex]x=\frac{-1}{3}[/tex] are zeros of our given quadratic function.
