Home
Class 12
MATHS
The equation x-2//x-1=1-2//x-1 has a. no...

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

A

no root

B

one root

C

two equal roots

D

infinitely many roots

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `x-(2)/(x-1)=1-(2)/(x-1)(2)/(x-1)impliesx=1`
But at `x=1` the given equation is not defined. Hence, no solution exist.
Promotional Banner

Similar Questions

Explore conceptually related problems

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 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 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)

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 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

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

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

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, There are exactly two distinct roots There is one pair of equation real roots. There are three pairs of equal roots Modulus of each root is 2