Q2 of 90 Page 2

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

8x2– 22x – 21

Let f(x) = 8x2 – 22x – 21


By splitting the middle term, we get


f(x) = 8x2 – 28x + 6x – 21


= 4x(2x – 7) + 3(2x – 7)


= (4x + 3) (2x – 7)


On putting f(x) = 0 , we get


(4x + 3) (2x – 7) = 0


⇒ 4x + 3 = 0 or 2x – 7 = 0


or


Thus, the zeroes of the given polynomial 8x2 – 22x – 21 are and


Verification


Sum of zeroes or



The product of zeroes or



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


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