Let `a , b , c` be three real numbers such that `a

Let a,b and c be three real numbers,such that a+2b+4c0. Then the equation ax^(2)+bx+c=0

Let a, b, c be three distinct real numbers such that each of the expressions ax^+bx +c, bx^2 + cx + a and ax^2 + bx + c are positive for all x in R and let alpha=(bc +ca+ab)/(a^2+b^2+c^2) then (A)alpha 1/4 (D) alpha>1

Let a,b,c be three non-zero real numbers such that the equation sqrt(3)a cos x+2b sin x=c,x in[-(pi)/(2),(pi)/(2)] has two distinct real roots alpha and beta with alpha+beta=(pi)/(3). Then,the value of (b)/(a) is

Let a,b and c be positive real numbers such that a+b+c=6. Then range of ab^(2)c^(3) is

If a, b and c are three real numbers such that a - b+c lt 1, a + b + c gt -1 and 9a + 3b + c lt -4 , then what is the sign of 'a' ?

Let a,b and c be three odd natural numbers such that a+b+c=11 then number of triplets of type(a,b,c ) is

Let a, b and c be real numbers such that 4a + 2b + c = 0 and ab gt 0. Then the equation ax^(2) + bx + c = 0 has