Q11 of 90 Page 2

Verify that the numbers given alongside of the cubic polynomial are their zeros. Also verify the relationship between the zeroes and the coefficients in each case :

x3 + 2x2 – x – 2; – 2 – 2, 1

Let p(x) = x3 + 2x2 – x – 2


Then, p( – 2) = ( – 2)3 + 2( – 2)2 – ( – 2) – 2


= – 8 + 8 + 2 – 2


= 0
p(1) = (1)3 + 2(1)2 – (1) – 2


= 1 + 2 – 1 – 2


= 0


Hence, – 2, – 2 and 1 are the zeroes of the given polynomial x3 + 2x2 – x – 2.


Now, Let α = – 2 , β = – 2 and γ = 1


Then, α + β + γ = – 2 + ( – 2) + 1 = – 3



αβ + βγ + γα = ( – 2)( – 2) + ( – 2)(1) + (1)( – 2)


= 4 – 2 – 2


= 0



and αβγ = ( – 2) × ( – 2) × 1


= 4



Thus, the relationship between the zeroes and the coefficients is not verified.


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