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 are positive real numbers, then the number of real roots of the equation ax^2+b|x|+c is

If a ,b ,c are distinct positive numbers, then the nature of roots of the equation 1//(x-a)+1//(x-b)+1//(x-c)=1//x is a. all real and is distinct b. all real and at least two are distinct c. at least two real d. all non-real

If a,b,c are real, then both the roots of the equation (x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0 are always (A) positive (B) negative (C) real (D) imaginary.

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 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

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 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 four consecutive terms of an increasing A.P., then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are a. non-real complex b. real and equal c. integers d. real and distinct

If a ,b ,c ,d are four consecutive terms of an increasing A.P., then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are a. non-real complex b. real and equal c. integers d. real and distinct

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