Equation `a^2/(x-alpha)+b^2(x-beta)+c^2/(x-gamma)=m-n^2x(a,b,c,m,n epsilon R)` has necessasrily (A) all the roots real (B) all the roots imaginary (C) two real and two imaginary roots (D) two rational two irrational roots

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

The equation x(x+2)(x ^2 −x)=−1 , has all roots imaginary ,neagative,two real two imaginary or all roots real.

The roots of the equations x ^2−x−3=0 are a. imaginary b. rational. c. irrational d. none of these.

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 0 gt a gt b gt c and the roots alpha, beta are imaginary roots of ax^(2) + bx + c = 0 then

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 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

Consider a quadratic equation az^2 + bz + c =0 where a, b, c, are complex numbers. Find the condition that the equation has (i) one purely imaginary root (ii) one purely real root (iii) two purely imaginary roots (iv) two purely real 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

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