Q2 of 90 Page 2

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

r2s2x2 + 6rstx + 9t2

Let f(x) = r2s2x2 + 6rstx + 9t2


Now, if we recall the identity


(a + b)2 = a2 + b2 + 2ab


Using this identity, we can write


r2s2x2 + 6rstx + 9t2 = (rsx + 3t)2


On putting f(x) = 0 , we get


(rsx + 3t)2 = 0



Thus, the zeroes of the given polynomial r2s2x2 + 6rstx + 9t2 are and


Verification


Sum of zeroes or



or



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


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