Q10 of 90 Page 2

Verify that are the zeroes of the cubic polynomial p(x) = 3x2 – 5x2 – 11x – 3 and then verify the relationship between the zeroes and the coefficients.

Let p(x) = 3 x3 – 5 x2 – 11x – 3


Then, p( – 1) = 3( – 1)3 – 5( – 1)2 – 11( – 1) – 3


= – 3 – 5 + 11 – 3


= 0





= 0


p(3) = 3(3)3 – 5(3)2 – 11(3) – 3


= 81 – 45 – 33 – 3


= 0


Hence, we verified that 3, – 1 and are the zeroes of the given polynomial.


So, we take α = 3, β = – 1,


Verification


α + β + γ



αβ + βγ + γα




and αβγ


= 1



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


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