Q2 of 90 Page 2

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

px2 + (2q – p2)x – 2pq, p≠0

Let f(x) = px2 + (2q – p2)x – 2pq


f(x) = px2 + 2qx – p2 x – 2pq


= x(px + 2q) – p(px + 2q)


= (x – p) (px + 2q)


On putting f(x) = 0, we get


(x – p) (px + 2q) = 0


⇒ x – p = 0 or px + 2q = 0


⇒x = p or =


Thus, the zeroes of the given polynomial px2 + (2q – p2)x – 2pq are p and


Verification


Sum of zeroes



Product of zeroes or



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


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