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Question 6
If one of the zeroes of the cubic polynomial x3+ax2+bx+c is -1, then the product of the other two zeros is
(A) b – a + 1
(B) b – a – 1
(C) a – b + 1
(D) a – b –1


Solution

Let p(x)=x3+ax2+bx+c
Let  α β  and γ be the zeroes of the given cubic polynomial p (x)
   α=1           [given]
and     p( - 1) = 0
 (1)3+a(1)2+b(1)+c=0
  1+ab+c=0
 c=1a+b
We know that,
Product of the zeroes = (1)3constant termcoefficient of x3=c1
αβγ=c
 (1)βγ=c        [α=1]
βγ=c
 βγ=1a+b     [fromEq.(i)]
Hence, product of the other two roots is 1 – a + b

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