The equation `x-2/(x-1)=1-2/(x-1)` has a. no root b. one root c. two equals roots d. Infinitely many 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 2 d. none of these

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

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

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

The number of values of k for which the equation x^3-3x+k=0 has two distinct roots lying in the interval (0,1) is three (b) two (c) infinitely many (d) zero

If b > a , then the equation (x-a)(x-b)-1=0 has (a) both roots in (a ,b) (b) both roots in (-oo,a) (c) both roots in (b ,+oo) (d)one root in (-oo,a) and the other in (b ,+oo)

If a ,b ,c in Ra n da b c<0 , then equation b c x^2+2(b+c-a)x+a=0h a s (a)both positive roots (b)both negative roots (c)real roots (d)one positive and one negative root

If alphaa n dbeta are the roots of x^2+p x+q=0a n dalpha^4,beta^4 are the roots of x^2-r x+s=0 , then the equation x^2-4q x+2q^2-r=0 has always. A. one positive and one negative root B . two positive roots C . two negative roots D . cannot say anything

For a , b , c non-zero, real distinct, the equation, (a^(2)+b^(2))x^(2)-2b(a+c)x+b^(2)+c^(2)=0 has non-zero real roots. One of these roots is also the root of the equation :

If a in (-1,1), then roots of the quadratic equation (a-1)x^2+a x+sqrt(1-a^2)=0 are a. real b. imaginary c. both equal d. none of these