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

If b_1. b_2=2(c_1+c_2) then at least one of the equation x^2+b_1x+c_1=0 and x^2+b_2x+c_2=0 has a) imaginary roots b) real roots c) purely imaginary roots 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

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

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 b gt 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)

A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)=x has no real roots. Prove that in this case equation P(P(x))=x has no real roots either.

For the equation |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=0, a) There are exactly two distinct roots b) There is one pair of equation real roots. c) There are three pairs of equal roots d) Modulus of each root is 2