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 :

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

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

The set of values of k for which x^(2)+(4k-1)x+9>0AA x in R is

If f(x)={{:(,ax^(2)-b,ale xlt 1),(,2,x=1),(,x+1,1 le xle2):} then the value of the pair (a,b) for which f(x) cannot be continuous at x=1, is

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

The least natural number a for which x+ax^(-2)>2AA x in(0,oo) is 1(b)2(c)5 (d) none of these