Question

Portia solved the quadratic equation x^2+(2sqrt(3))x+1=0 by completing the square. In the process, she came up with the equivalent equation : (x+r)^2 = s, where r and s are constants.

What is s?

Answer 1

Starting with x^2 + 2√3 x + 1 = 0, complete the square:
x^2 + 2√3 x + 1 = (x + √3)^2 - 3 + 1 = (x + √3)^2 - 2.

So (x + √3)^2 = 2, hence s = 2.