Q. 104.5( 13 Votes )
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.
Answer :
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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