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

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

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

Let f(x)= 3/(x-2)+4/(x-3)+5/(x-4) . Then f(x)=0 has (A) exactly one real root in (2,3) (B) exactly one real root in (3,4) (C) at least one real root in (2,3) (D) none of these

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 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

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 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

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

If 3(a+2c)=4(b+3d), then the equation a x^3+b x^2+c x+d=0 will have (a) no real solution (b) at least one real root in (-1,0) (c) at least one real root in (0,1) (d) none of these