Question

The roots of the function f(x) = x2 – 2x – 3 are shown. what is the missing number? x = –1 and x =

Answer 1

x^2 -2x -3 = 0

(x-3)(x+1)=0

x+1=0
x=-1

x-3=0
x = 3

so the missing number is 3

Answer 2

we have

`f(x)=x^(2)-2x-3`

Find the roots

Equate the function to zero

`x^(2)-2x-3=0`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`x^(2)-2x=3`

Complete the square. Remember to balance the equation by adding the same constants to each side.

`x^(2)-2x+1=3+1`

`x^(2)-2x+1=4`

Rewrite as perfect squares

`(x-1)^(2)=4`

Square root both sides

`(x-1)=(+/-)2`

`x=1(+/-)2`

`x=1+2=3`

`x=1-2=-1`

therefore

the answer is

`x=3`