Let there be a polynomial `p(x)=x^(3)-3x^(2)+4x-1` such that `p(a)=p(b)=p(c)=0"`and `a!=b!=c`. Find the value of `(2-a)(2-b)(2-c)`
`A)1`
`B)2 `
`C) 3`
`D) 4`

If alpha,\ beta are the zeros of the polynomial f(x)=x^2-p(x+1)-c such that (alpha+1)(beta+1)=0 , then c= (a) 1 (b) 0 (c) -1 (d) 2

Let P(x)=x^4+a x^3+b x^2+c x+d be a polynomial such that P(1)=1,P(2)=8,P(3)=27 ,P(4)=64 then the value of 152-P(5) is____________.

If zeros of the polynomial f(x)=x^3-3p x^2+q x-r are in A.P., then (a) 2p^3=p q-r (b) 2p^3=p q+r (c) p^3=p q-r (d) None of these

If the zeros of the polynomial f(x)=a x^3+3b x^2+3c x+d are in A.P., prove that 2b^3-3a b c+a^2d=0 .

If the polynomial f(x)=a x^3+b x-c is divisible by the polynomial g(x)=x^2+b x+c , then a b= (a) 1 (b) 1/c (c) -1 (d) -1/c

Let a,b,c, d be the roots of x ^(4) -x ^(3)-x ^(2) -1=0. Also consider P (x) =x ^(6)-x ^(5) -x ^(3) -x ^(2) -x, then the value of p (a) +p(b) +p(c ) +p(d) is equal to :

If alpha,\ beta are the zeros of the polynomial p(x)=4x^2+3x+7 , then 1/alpha+1/beta is equal to (a) 7/3 (b) -7/3 (c) 3/7 (d) -3/7

In Figure, the graph of a polynomial p(x) is shown. The number of zeroes of p(x) is (a)4 (b) 1 (c) 2 (d) 3

If x-a is a factor of x^3-3x^2a+2a^2x+b , then the value of b is (a) 0 (b) 2 (c) 1 (d) 3

If X is a Poisson variate such that P(X=2)=9P(X=4)+90P(X=6) , then mean of X is a) 1 b) 2 c) 1/2 d) 3/2