Which is a zero of the quadratic function f(x) = 9x2 – 54x – 19? x = (1)/(3) x = 3\frac{1}{3} x = 6\frac{1}{3} x = 9\frac{1}{3}

Question

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

x =
`(1)/(3)`
x = 3\frac{1}{3}
x = 6\frac{1}{3}
x = 9\frac{1}{3}

Answer 1

`x = 6(1)/(3)`

Explanation:

`f(x)=9x^2-54x-19\\0=9x^2-54x-19\\1=9x^2-54x-18\\1=9(x^2-6x-2)\\1+9(11)=9(x^2-6x-2+11)\\1+99=9(x^2-6x+9)\\100=9(x-3)^2\\(100)/(9)=(x-3)^2\\\pm(10)/(3)=x-3\\x=3\pm(10)/(3)\\\\x_1=3+(10)/(3)=6(1)/(3)\\\\x_2=3-(10)/(3)=-(1)/(3)`

Therefore, only the third option is the most applicable