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 < a < 2`
d . No real roots if `a<-1`

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

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 ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these

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 the equation a x^2+b x+c=x has no real roots, then the equation a(a x^2+b x+c)^2+b(a x^2+b x+c)+c=x will have a. four real roots b. no real root c. at least two least roots d. none of these

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)

The equation (x - 1)(x - 2)(x - 3) = 24 has the real root equal to 'a' and the complex roots b and c.Then the value of (bc)/a, is

Let a ,b ,cR_0 and each of the quadratic equations in x ,x^2+2(a^2+b^2)x+(b^2+c^2)^2=0 and x^2+2(b^2+c^2)x+(c^2+a^2)^2=0 has two distinct real roots. Then equation x^2+2(c^2+a^2)x+(a^2+b^2)^2=0 ha Two distinct positive real roots Two equal real roots Two distinct negative real roots (4) No real roots

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

Show that (x^2+1)^2-x^2=0 has no real roots.