The set that contains only the zeros of the function g is {x∈ R/x=±4/3}.
What is a Quadratic Function?
The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
For solving a quadratic function you should find the discriminant: [tex]D=b^2-4ac[/tex] and after that use this variable in the formula: [tex]x=\frac{-b\pm \sqrt{D} }{2a}[/tex]
For the given equation:a=9, b=0 and c=-16, like D=b²-4ac, you have:
D=0²-4*9*(-16)
D=576
After that, you should apply the formula [tex]x=\frac{-b\pm \sqrt{D} }{2a}[/tex]
[tex]x=\frac{-b\pm \sqrt{D} }{2a}\\ \\ x=\frac{-0\pm \sqrt{576} }{2*9}\\ \\ x=\frac{\pm \sqrt{576} }{18}=\frac{\pm 24 }{18}=\pm\frac{4}{3}[/tex]
Thus, x1=[tex]\frac{4}{3}[/tex] and x2=[tex]-\frac{4}{3}[/tex]
Read more about the quadratic function here:
brainly.com/question/1497716
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