Q3 of 90 Page 2

Find the zeroes of the quadratic polynomial 4 x2 – 4x – 3 and verify the relationship between the zeroes and the coefficients of the polynomial.

Let f(x) = 4 x2 – 4x – 3


By splitting the middle term, we get


f(x) = 4 x2 – 6x + 2x – 3


= 2x(2x – 3) + 1(2x – 3)


= (2x + 1) (2x – 3)


On putting f(x) = 0, we get


(2x + 1) (2x – 3) = 0


⇒ 2x + 1 = 0 or 2x – 3 = 0


or


Thus, the zeroes of the given polynomial4x2 – 4x – 3 are and


Verification


Sum of zeroes or



Product of zeroes or



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


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