Which is a zero of the quadratic function f(x) = 9x2 – 54x – 19?x = x = 3x = 6x = 9

Accepted Solution

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] Β  Β  [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 Β [tex]x=\frac{-1}{3}[/tex] are zeros of our given quadratic function.