Question

Which constant should be added and subtracted to solve the quadratic equation `4"x"^2 - sqrt3"x" - 5` = 0 by the method of completing the square?

Options

• `9/16`

• `3/16`

• `3/4`

• `sqrt3/4`

Answer 1

`3/16`

Explanation:

This can be written as

`4"x"^2 - sqrt3"x" - 5` = 0

`(2"x")^2 - 2 xx (2"x") xx sqrt3/4 - 5 + (sqrt3/4)^2 - (sqrt3/4)^2` = 0

`(2"x")^2 - 2 xx (2"x") xx sqrt3/4 + (sqrt3/4)^2 - 5 - 3/16` = 0

`(2"x" - sqrt3/4)^2 = 5 + 3/16`

`(2"x" - sqrt3/4)^2 = 83/16`

Hence the given equation can be solved by adding and subtracting `3/16`.