Find the zeroes o

Let f(x) = √3 x² – 8x + 4√3

By splitting the middle term, we get

(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)

or

Thus, the zeroes of the given polynomial√3 x² – 8x + 4√3 are and 2

Verification

Sum of zeroes or

Product of zeroes or

So, the relationship between the zeroes and the coefficients is verified.