Question

Write x2 - 2x - 3 = 0 in the form (x - a)2 = b, where a and b are integers. (x - 4)2 = 3 (x - 3)2 = 2 (x - 2)2 = 1 (x - 1)2 = 4

Answer 1

`f(x)=x^(2)-2x-3 \\ \\ \Delta=(-2)^(2)-4*1*(-3)=4+12=16 \\ \\ a= (2)/(2)=1 \\ \\ b= (-16)/(4)=-4 \\ \\ x^(2)-2x-3=(x-1)^(2)-4=(x-1)^(2)=4`

\\\ Ben

Answer 2

The correct option is 4.

Explanation:

The given equation is

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

If an expression is
`x^2+bx`, then to make it perfect sqaure add
`((b)/(2))^2`.

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

Here b=-2,to make the perfect square we need to add
`((-2)/(2))^2`,i.e, 1.

`(x^2-2x+1)-1-3=0`

`(x-1)^2-4=0`
`[\because (a-b)^2=a^2-2ab+b^2]`

Add 4 on both the sides.

`(x-1)^2-4+4=0+4`

`(x-1)^2=4`

Therefore the correct option is 4.