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,q be non zero real numbes and f(x)!=0, in [0,2] and int_0^1 f(x).(x^2+px+q)dx=int_0^2 f(x).(x^2+px+q)dx=0 then equation x^2+px+q=0 has (A) two imginary roots (B) no root in (0,2) (C) one root in (0,1) and other in (1,2) (D) one root in (-oo,0) and other in (2,oo)

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

Find the values of p for which the equation x^(4)-14x^(2)+24x-3-p=0 has (a) Two distinct negative real roots (b) Two real roots of opposite sign (c) Four distinct real roots (d) No real roots

If f(x) is continuous in [0,2] and f(0)=f(2) then the equation f(x)=f(x+1) has (A) one real root in [0,2](B) atleast one real root in [0,1](C) atmost one real root in [0,2](D) atmost one real root in [1,2]

The equation x^(5)+x^(4)+1=0 has (1) One real and four imaginary roots (2) Five real roots (3) Three real and two imaginary roots (4) Three real roots in which two are same and two imaginary 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

Let f(x)=x^3+x^2+10x+7sinx, then the equation 1/(y-f(1))+2/(y-f(2))+3/(y-f(3))=0 has (A) no real root (B) one real roots (C) two real roots (D) more than two real roots

The equation (x/(x+1))^2+(x/(x-1))^2=a(a-1) has a. Four real roots if a >2 b.Four real roots if a<-1 c Two real roots if 1

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

(x^(2)+1)^(2)-x^(2)=0 has (i) four real roots (ii) two real roots (iii) no real roots (iv) one real root