Answer: The required number is 3.
Step-by-step explanation: Given that the roots of the function [tex]f(x)=x^2-2x-3[/tex] are shown below :
[tex]x=-1,x=?[/tex]
We are to find the missing number.
To find the missing number, we must solve the quadratic equation f(x) = 0.
We have
[tex]f(x)=0\\\\\Rightarrow x^2-2x-3=0\\\\\Rightarrow x^2-3x+x-3=0\\\\\Rightarrow x(x-3)+1(x-3)=0\\\\\Rightarrow (x+1)(x-3)=0\\\\\Rightarrow x+1=0,x-3=0\\\\\Rightarrow x=-1,3.[/tex]
Therefore, the roots of the given equation are x = -1 and x = 3.
Thus, the required number is 3.
