Question

What number must be added to x^2+6x+7 to form a perfect square

Answer 1

Let the number be k,

Then adding to the expression we have,


`{x}^(2) + 6x + 7 + k`
For this to be a perfect square, the discriminant must be zero.

We have,


`a=1, b=6, c=7+k`



`{b}^(2) - 4ac = 0`

This implies that


`{6}^(2) - 4(1)(7 +k ) = 0`

`36 - 28 - 4k = 0`

`8 - 4k = 0`

`8 = 4k`

`k = 2`
hence the number to be added is 2