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 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 non zero rational no then prove roots of equation (a b c^2)x^2+3a^2c x+b^2c x-6a^2-a b+2b^2=0 are rational.

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

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 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 ax^3+bx^2+cx+d has local extremum at two points of opposite signs then roots of equation ax^2+bx+c=0 are necessarily (A) rational (B) real and unequal (C) real and equal (D) imaginary

If a ,b ,c in R^+a n d2b=a+c , then check the nature of roots of equation a x^2+2b x+c=0.