Answer:
Option (3) is correct.
The zero of given function [tex]f(x)=x^2+4x+3[/tex] is x= -1 and x= -3.
Step-by-step explanation:
Consider the given function [tex]f(x)=x^2+4x+3[/tex]
We need to find the zero of the above function. Put f(x)=0
then , [tex]f(x)=x^2+4x+3=0 \Rightarrow x^2+4x+3=0[/tex]
The above function represents a quadratic equation
We can solve the quadratic equation by splitting middle term method,
[tex]\Rightarrow x^2+4x+3=0[/tex]
We can write 4x as x+ 3x ,
[tex]\Rightarrow x^2+x+3x+3=0[/tex]
[tex]\Rightarrow x(x+1)+3(x+1)=0[/tex]
[tex]\Rightarrow (x+1)(x+3)=0[/tex]
[tex]\Rightarrow (x+1)=0[/tex] or [tex]\Rightarrow (x+3)=0[/tex]
[tex]\Rightarrow x=-1[/tex] or [tex]\Rightarrow x=-3[/tex]
Thus, the zero of given function [tex]f(x)=x^2+4x+3[/tex] is x= -1 and x= -3.
