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 rational numbers a,b,c be th pth, qth, rth terms respectively of an A.P. then roots of the equation a(q-r)x^2+b(r-p)x+c(p-q)=0 are necessarily (A) imaginary (B) rational (C) irrational (D) real and equal

If a,b,c are rational then roots of equation abc^2x^2+3a^2 cx+b^2 cx-6a^2-ab+2b^2=0 are (A) irrational (B) rational (C) imaginary (D) irrational if a^2ltb

If two distinct chords drawn from the point (a, b) on the circle x^2+y^2-ax-by=0 (where ab!=0) are bisected by the x-axis, then the roots of the quadratic equation bx^2 - ax + 2b = 0 are necessarily. (A) imaginary (B) real and equal (C) real and unequal (D) rational

If a,b,c,d are unequal positive numbes, then the roots of equation x/(x-a)+x/(x-b)+x/(x-c)+x+d=0 are necessarily (A) all real (B) all imaginary (C) two real and two imaginary roots (D) at least two real

If a,b,c,d are in G.P., then the value of (a-c)^2+(b-c)^2+(b-d)^2-(a-d)^2 is (A) 0 (B) 1 (C) a+d (D) a-d

If the chord of contact of the tangents from a point on the circle x^2 + y^2 = a^2 to the circle x^2 + y^2 = b^2 touch the circle x^2 +y^2 = c^2 , then the roots of the equation ax^2 + 2bx + c = 0 are necessarily. (A) imaginary (B) real and equal (C) real and unequal (D) rational

If a, b, c, d are in G.P., then prove that: (b-c)^(2)+(c-a)^(2)+(d-b)^(2)=(a-d)^(2)

If a+b+c=0 and a,b,c are ratiional. Prove that the roots of the equation (b+c-a)x^(2)+(c+a-b)x+(a+b-c)=0 are rational.