Q. 3 C5.0( 5 Votes )
Find the zeroes of the quadratic polynomial √3 x2 – 8x + 4√3 .
Answer :
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.
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