which is a zero of the quadratic function f(x) = 9x² - 54x - 19?\no x = 1/3\no x = 3 1/3\no x = 6 1/3\no x =…

Explanation:

Step1: Recall the zero - definition

A zero of a function (f(x)) is a value of (x) for which (f(x)=0). We can check each option by substituting the value of (x) into the function (f(x)=9x^{2}-54x - 19).

Step2: Check (x = \frac{1}{3})

Substitute (x=\frac{1}{3}) into (f(x)): [ \begin{align*} f(\frac{1}{3})&=9\times(\frac{1}{3})^{2}-54\times\frac{1}{3}-19\ &=9\times\frac{1}{9}-18 - 19\ &=1-18 - 19\ &=-36 \end{align*} ]

Step3: Check (x = 3\frac{1}{3}=\frac{10}{3})

Substitute (x = \frac{10}{3}) into (f(x)): [ \begin{align*} f(\frac{10}{3})&=9\times(\frac{10}{3})^{2}-54\times\frac{10}{3}-19\ &=9\times\frac{100}{9}-180 - 19\ &=100-180 - 19\ &=-99 \end{align*} ]

Step4: Check (x = 6\frac{1}{3}=\frac{19}{3})

Substitute (x=\frac{19}{3}) into (f(x)): [ \begin{align*} f(\frac{19}{3})&=9\times(\frac{19}{3})^{2}-54\times\frac{19}{3}-19\ &=9\times\frac{361}{9}-342-19\ &=361-342 - 19\ &=0 \end{align*} ]

Step5: Check (x = 9\frac{1}{3}=\frac{28}{3})

Substitute (x=\frac{28}{3}) into (f(x)): [ \begin{align*} f(\frac{28}{3})&=9\times(\frac{28}{3})^{2}-54\times\frac{28}{3}-19\ &=9\times\frac{784}{9}-504 - 19\ &=784-504 - 19\ &=261 \end{align*} ]

Answer:

(x = 6\frac{1}{3})