Let f(x) = √3 x2 – 8x + 4√3
By splitting the middle term, we get
f(x) = √3 x2 – 6x – 2x + 4√3
= √3 x(x – 2√3) – 2(x – 2√3)
= (√3 x – 2) (x – 2√3)
On putting f (x) = 0, we get
(√3 x – 2) (x – 2√3) = 0
⇒ √3 x – 2 = 0 or x – 2√(3 = 0)
x = 2/√3 or x = 2√3
Thus, the zeroes of the given polynomial√3 x2 – 8x + 4√3 are 2/√3 and 2√3
Verification
So, the relationship between the zeroes and the coefficients is verified.