Home
Class 12
MATHS
Find the complete set of values of a suc...

Find the complete set of values of a such that `(x^2-x)//(1-a x)` attains all real values.

Text Solution

Verified by Experts

The correct Answer is:
` ain [1, infty)` ,
`y= (x^(2) - x)/ (1 - ax)`
or `x^(2) - x = y - axy`
or ` x^(2) + x (ay - 1) - y = 0`
Since x is real, so
`(ay - 1)^(2) + 4y ge 0`
`rArr a^(2) y^(2) + 2y (2-a) + 1 ge 0, AA y in ` R
`rArr a^(2) gt 0, 4(2 - a)^(2) - 4a^(2) le 0 rArr 4 - 4a le 0 rArr a in [ 1 , infty)` .
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.13|9 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise Single Correct Answer Type : Exercise|89 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.11|8 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

The complete set of real values of 'a' such that the point lies triangle p(a, sin a) lies inside the triangle formed by the lines x-2y +2= 0; x+y=0 and x-y-pi=0

Find the set of values of x for which (tan 3x - tan 2x)/(1 + tan 3x cdot tan 2x) = 1

Find the set of all x for which : (2x)/(2x^2+5x+2)gt1/(x+1)

The complete set of values of x for which (x^(3)(x-1)^(2)(x+4))/((x+1)(x-3)) ge 0 is

Find the set of real value(s) of a for which the equation |2x+3|+|2x-3|=a x+6 has more than two solutions.

Find the value of a in order that f(x)=sqrt(3)sinx-cosx-2a x+b decreases for all real values of xdot

Find all the possible values of 1/x for x>3 .

If f(x)=|x-2|+|x-4|+|x-6| . Find the set of value of x such that f(x) is increases

Complete set of values of x satisfying inequality ||x-1|-5| lt 2x -5 is

If f(x)=|x-2|+|x-4|+|x-6| . Find the set of value of x such that f(x) is decreasing