Answer:
The zeros of the function are [tex]\frac{5}{3}[/tex] and [tex]\frac{4}{3}[/tex].
Step-by-step explanation:
The given function is
[tex]f(x)=9x^2-27x+20[/tex]
Equate f(x)=0 to find the zeroes of the function.
[tex]9x^2-27x+20=0[/tex]
Using splitting the middle terms method, the middle term can be written as -15x-12x.
[tex]9x^2+(-15x-12x)+20=0[/tex]
[tex](9x^2-15x)+(-12x+20)=0[/tex]
Taking out common factors from each parenthesis.
[tex]3x(3x-5)-4(3x-5)=0[/tex]
[tex](3x-5)(3x-4)=0[/tex]
Using zero product property, we get
[tex]3x-5=0\Rightarrow x=\frac{5}{3}[/tex]
[tex]3x-4=0\Rightarrow x=\frac{4}{3}[/tex]
Therefore the zeros of the function are [tex]\frac{5}{3}[/tex] and [tex]\frac{4}{3}[/tex].
