The number of pairs (a, b) for which `a(x+1)^2+b(x^2-3x-2)+x+1=0 AA x in R` is :

Find the number of values of the pair (a,b) for which a(x+1)^(2)+b(x^(2)-3x-2)+x+1= 0 AA x in R

The number of values of the pair (a,b) for which a(x+1)^(2)+b(-x^(2)3x-2)+x+1=0 is an identity in x, is

The number of values of the pair (a, b) for which a(x+1)^2 + b(-x^2 – 3x - 2) + x + 1 = 0 is an identity in x, is

Number of integral values of 'a' for which (a-1)x^(2)+(a-1)x+1>=0AA x in R ,is ?

Suppose a in R . Define f and g as follows: f(x) =(a^(2) - 4a + 3)x^(2) + (a^(2) -1)a AA x in R and g(x) = (a^(2) - 5a + 6)x^(3) + (a^(2) -3a+ 2)x + (a^(3) -1) AA x in R The number of values of a for which f(x) = g(x) AA x in R

Find the values of k for which |(x^(2)+kx+1)/(x^(2)+x+1)|<2,AA x in R

The number of linear functions f satisfying f(x+f(x))= x + f (x) AA x in R is a)0 b)1 c)2 d)3

The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,4x^2,1+8x^3] , [3x, 9x^2,1+27x^3]|=10 is (A) 0 (B) 1 (C) 2 (D) 3

The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,4x^2,1+8x^3] , [3x, 9x^2,1+27x^3]|=10 is (A) 0 (B) 1 (C) 2 (D) 3