Q2 of 90 Page 2

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

10x2 + 3x – 1

Let f(x) = 10x2 + 3x – 1


By splitting the middle term, we get


f(x) = 10x2 – 2x + 5x – 1


= 2x(5x – 1) + 1(5x – 1)


= (2x + 1) (5x – 1)


On putting f(x) = 0, we get


(2x + 1) (5x – 1) = 0


⇒ 2x + 1 = 0 or 5x – 1 = 0


= or =


Thus, the zeroes of the given polynomial10x2 + 3x – 1 are and


Verification


Sum of zeroes



Product of zeroes or



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


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