Let f (x) = x2 – 3
Now, if we recall the identity
(a2 – b2) = (a – b)(a + b)
Using this identity, we can write
x2 – 3 = (x – √3) (x + √3)
So, the value of x2 – 3 is zero when x = √3 or x = – √3
Therefore, the zeroes of x2 – 3 are √3 and – √3.
Verification
Now,
So, the relationship between the zeroes and the coefficients is verified.