Q1 of 90 Page 2

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients:

3x2 + 5x – 2

Let f(x) = 3x2 + 5x – 2


By splitting the middle term, we get


f(x) = 3x2 + (6 – 1)x – 2 [∵ 5 = 6 – 1 and 2×3 = 6]


= 3x2 + 6x – x – 2


= 3x(x + 2) – 1(x + 2)


= (3x – 1) (x + 2)


On putting f(x) = 0 , we get


(3x – 1) (x + 2) = 0


⇒ 3x – 1 = 0 or x + 2 = 0


or x = – 2


Thus, the zeroes of the given polynomial 3x2 + 5x – 2 are – 2 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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