Answer:
Option 4th is correct
x = 3, -1
Step-by-step explanation:
Given the equation:
[tex]f(x) = x^2-2x-3[/tex]
To find the zeroes of f(x).
Set f(x) = 0
then;
[tex]x^2-2x-3 = 0[/tex]
Factorize this equations:
Split the middle terms we have;
[tex]x^2-3x+x-3 = 0[/tex]
⇒[tex]x(x-3)+1(x-3)= 0[/tex]
⇒[tex](x-3)(x+1)= 0[/tex]
By zero product property we have;
x-3 = 0 and x+1 = 0
⇒x = 3 and x = -1
Therefore, the zeroes of the function f(x) are :
x = 3 and x = -1
