Answer:
[tex]\bf \displaystyle\frac{5+1}{2}=\displaystyle\frac{6}{2}=3[/tex]
Step-by-step explanation:
The x-intercepts are the values of x for which y=0, that is f(x)=0.
The x-intercepts of
[tex]\bf f(x)=4x^2-24x+20[/tex]
are the values of x such that
[tex]\bf 4x^2-24x+20=0[/tex]
Divide both sides by 4 to simplify a little
[tex]\bf x^2-6x+5=0[/tex]
Solve the quadratic equation
[tex]\bf x=\displaystyle\frac{-(-6)\pm\sqrt{(-6)^2-4*1*5}}{2*1}=\displaystyle\frac{6\pm\sqrt{36-20}}{2}=\\\\=\displaystyle\frac{6\pm\sqrt{16}}{2}=\displaystyle\frac{6\pm4}{2}[/tex]
and you get the 2 x-intercepts
x =10/2 and x = 2/2
or
x = 5 and x = 1
The average is the midpoint
[tex]\bf \displaystyle\frac{5+1}{2}=\displaystyle\frac{6}{2}=3[/tex]
