we know that
The zeros of the function are the values of x when the value of the function is equal to zero
so
Let's verify each case to determine the solution.
Substitute the value of \(x=3\) and \(x=7\) in each function and then verify the value of the function
case A) \(f(x)=x^{2} +4x-21\)
For \(x=3\)
\(f(3)=3^{2} +4*3-21=0\)
therefore
the value of \(x=3\) is a zero of the function
For \(x=7\)
\(f(7)=7^{2} +4*7-21=56\)
therefore
the value of \(x=7\) is not a zero of the function
The case A) is not the solution
case B) \(f(x)=x^{2} -4x-21\)
For \(x=3\)
\(f(3)=3^{2} -4*3-21=-24\)
therefore
the value of \(x=3\) is not a zero of the function
For \(x=7\)
\(f(7)=7^{2} -4*7-21=0\)
therefore
the value of \(x=7\) is a zero of the function
The case B) is not the solution
case C) \(f(x)=x^{2} -10x+21\)
For \(x=3\)
\(f(3)=3^{2} -10*3+21=0\)
therefore
the value of \(x=3\) is a zero of the function
For \(x=7\)
\(f(7)=7^{2} -10*7+21=0\)
therefore
the value of \(x=7\) is a zero of the function
The case C) is a solution
case D) \(f(x)=x^{2} -10x-21\)
For \(x=3\)
\(f(3)=3^{2} -10*3-21=-42\)
therefore
the value of \(x=3\) is not a zero of the function
For \(x=7\)
\(f(7)=7^{2} -10*7-21=-42\)
therefore
the value of \(x=7\) is not a zero of the function
The case D) is not a solution
therefore
The answer is
\(f(x)=x^{2} -10x+21\)
