If the equation `ax^2+bx+c=x^3+1/x(a.b.c<=0)`has only real roots and all the roots are integers then the value of `(-a-b-c)/7` is

If the equations ax^(2)+bx+c=0 and x^(2)+x+1=0 has one common root then a:b:c is equal to

If the equation ax^(2)+bx+c=x has no real roots,then the equation a(ax^(2)+bx+c)^(2)+b(ax^(2)+bx+c)+c=x will have a.four real roots b.no real root c.at least two least roots d.none of these

If a root of the equation ax^(2)+bx+c=0 be reciprocal of a root of the equation a'x^(2)+b'x+c'=0 then

If the equations ax^(2)+bx+C=0 and x^(2)+2x+4=0 have a common root then find a:b:c

If the given equation ax^2+bx+c=0 and the equation x^2+2x+9=0 have a common root, then a:b:c is (A) 1:2:9 (B) 1:2:3 (C) 1:1:1 (D) none of these

Let a, b, c in R with a gt 0 such that the equation ax^(2) + bcx + b^(3) + c^(3) - 4abc = 0 has non-real roots. If P(x) = ax^(2) + bx + c and Q(x) = ax^(2) + cx + b , then

Let a, b, c in R with a gt 0 such that the equation ax^(2) + bcx + b^(3) + c^(3) - 4abc = 0 has non-real roots. If P(x) = ax^(2) + bx + c and Q(x) = ax^(2) + cx + b , then

If one root of the equations ax^(2)+bx+c=0 and bx^(2)+cx+a=0, (a, b, c in R) is common, then the value of ((a^(3)+b^(3)+c^(3))/(abc))^(3) is