Question

Please help:What are the zeros of the function?f (x) = 3x^2 − 24x + 36Enter your answers in the boxes.The zeros of f(x) are __ and ___.

Answer 1

Answer

The zeros of f(x) are 2 and 6

Step-by-step explanation

The function:

$f(x)=3x^2-24x+36$

has the form:

$f(x)=ax^2+bx+c$

with the constants: a = 3, b = -24, and c = 36.

We can find the zeros of f(x) with the help of the quadratic formula, as follows:

$\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x_{1,2}=\frac{24\pm\sqrt{(-24)^2-4\cdot3\operatorname{\cdot}36}}{2\cdot3} \\ x_{1,2}=\frac{24\pm\sqrt{144}}{6} \\ x_1=\frac{24+12}{6}=6 \\ x_2=\frac{24-12}{6}=2 \end{gathered}$