If a,b,c are rational and are in G.P and `a-b, c-a, b-c` are in H.P. then the equations `ax^2+4bx-c=0 and a(b-c)x^2+b(c-a)x+c(a-b)=0` have (A) imaginary roots (B) irrational roots (C) rational roots (D) a common root

If a, b, c are rational and the tangent to the parabola y^2 = 4kx , at P(p, q) and Q(q, b) meet at R(r, c) , then the equation ax^2 + bx-2c=0 has (A) imaginary roots (B) real and equal roots (C) rational roots (D) irrational roots

If a,b,c,d are rational and are in G.P. then the rooots of equation (a-c)^2 x^2+(b-c)^2x+(b-x)^2-(a-d)^2= are necessarily (A) imaginary (B) irrational (C) rational (D) real and equal

If a, b and c are in AP and if the equations (b-c)x^2 + (c -a)x+(a-b)=0 and 2 (c +a)x^2+(b +c)x+(a-b)=0 have a common root, then

If a, b, c are in GP , then the equations ax^2 +2bx+c = 0 and dx^2 +2ex+f =0 have a common root if d/a , e/b , f/c are in

If the equation ax^2+2bx+c=0 and ax^2+2cx+b=0 b!=c have a common root ,then a/(b+c =

If p and q are odd integers, then the equation x^2+2px+2q=0 (A) has no integral root (B) has no rational root (C) has no irrational root (D) has no imaginary root

If a,b,c are in A.P. then the roots of the equation (a+b-c)x^2 + (b-a) x-a=0 are :

If b_1. b_2=2(c_1+c_2) then at least one of the equation x^2+b_1x+c_1=0 and x^2+b_2x+c_2=0 has a) imaginary roots b) real roots c) purely imaginary roots d) none of these

If a,b,c in R and the equation ax^2+bx+c = 0 and x^2+ x+ 1=0 have a common root, then

Let a,b,c be real numbers in G.P. such that a and c are positive , then the roots of the equation ax^(2) +bx+c=0