If `0ltalphaltbetaltgammaltpi/2` then the equation `1/(x-sinalpha)+1/(x-sinbeta)+1/(x-singamma)=0` has
(A) imaginary roots
(B) real and equal roots
(C) real and unequal roots
(D) rational roots

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

Equation a/(x-1)+b/(x-2)+c/(x-3)=0(a,b,cgt0) has (A) two imaginary roots (B) one real roots in (1,2) and other in (2,3) (C) no real root in [1,4] (D) two real roots in (1,2)

If f(x)=x has non real roots, then the equation f(f(x))=x (A) has all real and unequal roots (B) has some real and non real roots (C) has all real and equal roots (D) has all non real roots

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 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 p,q,r epsilon R and are distinct the equation (x-p)^5+(x-q)^5+(x-r)^5=0 has (A) four imaginary and one real root (B) two imaginary and three real roots (C) all the roots real (D) none of these

The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has A. only purely imaginary roots B. all real roots C. two real and purely imaginary roots D. neither real nor purely imaginary roots

The quadratic equation 2x^(2)-sqrt5x+1=0 has (a) two distinct real roots (b) two equal real roots (c) no real roots (d) more than 2 real roots

The equation 7x^(2)-(7pi+22)x+22pi=0has (A) equal roots (B) a root which is negative (C) rational roots only (D) a rational root and an irrational root.

-If a,b,c in R then prove that the roots of the equation 1/(x-a)+1/(x-b)+1/(x-c)=0 are always real cannot have roots if a=b=c