Q3 of 90 Page 2

Find the zeroes of the quadratic polynomial √3 x2 – 8x + 4√3 .

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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