Maths-
General
Easy

Question

fraction numerator 3 x squared plus x plus 1 over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end fraction equals fraction numerator a over denominator left parenthesis x minus 1 right parenthesis end fraction plus fraction numerator b over denominator left parenthesis x minus 1 right parenthesis squared end fraction plus fraction numerator c over denominator left parenthesis x minus 1 right parenthesis cubed end fraction plus fraction numerator d over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end fraction text  then  end text open square brackets table attributes columnalign left left columnspacing 1em end attributes row cell a      b end cell row cell c      d end cell end table close square brackets equals

  1. open square brackets table attributes columnalign left left columnspacing 1em end attributes row cell 3      7 end cell row cell 5      0 end cell end table close square brackets
       
  2. open square brackets table attributes columnalign left left columnspacing 1em end attributes row cell 0      3 end cell row cell 7      5 end cell end table close square brackets    
  3. open square brackets table attributes columnalign left left columnspacing 1em end attributes row cell 0      7 end cell row cell 3      5 end cell end table close square brackets  
  4. open square brackets table attributes columnalign left left columnspacing 1em end attributes row cell 3      5 end cell row cell 7      0 end cell end table close square brackets    

The correct answer is: open square brackets table attributes columnalign left left columnspacing 1em end attributes row cell 0      3 end cell row cell 7      5 end cell end table close square brackets


    fraction numerator 3 x squared plus x plus 1 over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end fraction equals fraction numerator a over denominator left parenthesis x minus 1 right parenthesis end fraction plus fraction numerator b over denominator left parenthesis x minus 1 right parenthesis squared end fraction plus fraction numerator c over denominator left parenthesis x minus 1 right parenthesis cubed end fraction plus fraction numerator d over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end fraction
fraction numerator 3 x squared plus x plus 1 over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end fraction equals fraction numerator a left parenthesis x minus 1 right parenthesis cubed plus b left parenthesis x minus 1 right parenthesis squared plus c left parenthesis x minus 1 right parenthesis plus d over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end fraction
3 x squared plus x plus 1 equals a left parenthesis x minus 1 right parenthesis cubed plus b left parenthesis x minus 1 right parenthesis squared plus c left parenthesis x minus 1 right parenthesis plus d
3 x squared plus x plus 1 equals a left parenthesis x cubed minus 3 x squared plus 2 x minus 1 right parenthesis plus b left parenthesis x squared minus 2 x plus 1 right parenthesis plus c left parenthesis x minus 1 right parenthesis plus d
3 x squared plus x plus 1 equals a x cubed minus 3 a x squared plus 2 a x minus a plus b x squared minus 2 b x plus b plus c x minus c plus d
3 x squared plus x plus 1 equals a x cubed plus open parentheses b minus 3 a close parentheses x squared plus open parentheses 2 a minus 2 b plus c close parentheses x plus open parentheses b plus d minus a minus c close parentheses
C o m p a r i n g space c o e f f i c i e n t s space o n space b o t h space t h e space s i d e s comma
rightwards double arrow a equals 0 space space space..... open parentheses 1 close parentheses
rightwards double arrow b minus 3 a equals 3
F r o m space e q u a t i o n space 1 comma
b minus 3 open parentheses 0 close parentheses equals 3
therefore b equals 3 space space space.... open parentheses 2 close parentheses
rightwards double arrow 2 a minus 2 b plus c equals 1
F r o m space e q u a t i o n space 1 space a n d space 2 comma
2 open parentheses 0 close parentheses minus 2 open parentheses 3 close parentheses plus c equals 1
minus 6 plus c equals 1
c equals 1 plus 6
therefore c equals 7 space space space.... open parentheses 3 close parentheses
rightwards double arrow b plus d minus a minus c equals 1
3 plus d minus 0 minus 7 equals 1
minus 4 plus d equals 1
d equals 1 plus 4
therefore d equals 5 space space space.... open parentheses 4 close parentheses

S o comma
open square brackets table row a b row c d end table close square brackets equals open square brackets table row 0 3 row 7 5 end table close square brackets

    Related Questions to study

    General
    Maths-

    If vertical line x vertical line less than 1 fifth, the coefficient of x cubed in the expansion of  fraction numerator 1 over denominator left parenthesis 1 minus 5 x right parenthesis left parenthesis 1 minus 4 x right parenthesis end fraction is

    If vertical line x vertical line less than 1 fifth, the coefficient of x cubed in the expansion of  fraction numerator 1 over denominator left parenthesis 1 minus 5 x right parenthesis left parenthesis 1 minus 4 x right parenthesis end fraction is

    Maths-General
    General
    maths-

    If a subscript K equals fraction numerator 1 over denominator K left parenthesis K plus 1 right parenthesis end fractionfor K equals 1 comma 2 comma 3 horizontal ellipsis.. n  then open parentheses sum from K equals 1 to n of   a subscript K close parentheses squared equals

    If a subscript K equals fraction numerator 1 over denominator K left parenthesis K plus 1 right parenthesis end fractionfor K equals 1 comma 2 comma 3 horizontal ellipsis.. n  then open parentheses sum from K equals 1 to n of   a subscript K close parentheses squared equals

    maths-General
    General
    Maths-

    The number of partial fractions of  fraction numerator 2 over denominator x to the power of 4 plus x squared plus 1 end fractionis

    The number of partial fractions of  fraction numerator 2 over denominator x to the power of 4 plus x squared plus 1 end fractionis

    Maths-General
    parallel
    General
    maths-

    The number of partial fractions of fraction numerator x cubed minus 3 x squared plus 3 x over denominator left parenthesis x minus 1 right parenthesis to the power of 5 end fraction is

    The number of partial fractions of fraction numerator x cubed minus 3 x squared plus 3 x over denominator left parenthesis x minus 1 right parenthesis to the power of 5 end fraction is

    maths-General
    General
    maths-

    Coefficient of x cubed y to the power of 4 z squared is left parenthesis 2 x minus 3 y plus 4 z right parenthesis to the power of 9 is

    Coefficient of x cubed y to the power of 4 z squared is left parenthesis 2 x minus 3 y plus 4 z right parenthesis to the power of 9 is

    maths-General
    General
    maths-

    Coefficient of x to the power of r is 1 plus left parenthesis 1 plus x right parenthesis plus left parenthesis 1 plus x right parenthesis squared plushorizontal ellipsis plus left parenthesis 1 plus x right parenthesis to the power of n is

    Coefficient of x to the power of r is 1 plus left parenthesis 1 plus x right parenthesis plus left parenthesis 1 plus x right parenthesis squared plushorizontal ellipsis plus left parenthesis 1 plus x right parenthesis to the power of n is

    maths-General
    parallel
    General
    maths-

    If a,b,c,d are consective binomial coefficients of left parenthesis 1 plus x right parenthesis to the power of n then fraction numerator a plus b over denominator a end fraction comma fraction numerator b plus c over denominator b end fraction comma fraction numerator c plus d over denominator c end fraction are is

    If a,b,c,d are consective binomial coefficients of left parenthesis 1 plus x right parenthesis to the power of n then fraction numerator a plus b over denominator a end fraction comma fraction numerator b plus c over denominator b end fraction comma fraction numerator c plus d over denominator c end fraction are is

    maths-General
    General
    maths-

    No of terms whose value depend on 'x' is left parenthesis x squared minus 2 plus 1 divided by x squared right parenthesis to the power of n is

    No of terms whose value depend on 'x' is left parenthesis x squared minus 2 plus 1 divided by x squared right parenthesis to the power of n is

    maths-General
    General
    Maths-

    If T subscript 0 comma T subscript 1 comma T subscript 2 comma horizontal ellipsis. T subscript n represent the terms is left parenthesis x plus a right parenthesis to the power of n then left parenthesis T subscript 0 minus T subscript 2 plus T subscript 4 minus T subscript 6 plus midline horizontal ellipsis right parenthesis squared plusleft parenthesis T subscript 1 minus T subscript 3 plus T subscript 5 minus horizontal ellipsis right parenthesis squared  is

    If T subscript 0 comma T subscript 1 comma T subscript 2 comma horizontal ellipsis. T subscript n represent the terms is left parenthesis x plus a right parenthesis to the power of n then left parenthesis T subscript 0 minus T subscript 2 plus T subscript 4 minus T subscript 6 plus midline horizontal ellipsis right parenthesis squared plusleft parenthesis T subscript 1 minus T subscript 3 plus T subscript 5 minus horizontal ellipsis right parenthesis squared  is

    Maths-General
    parallel
    General
    Maths-

    Let ' O be the origin and A be a point on the curve y to the power of 2 end exponent equals 4 x then locus of the midpoint of OA is

    Let ' O be the origin and A be a point on the curve y to the power of 2 end exponent equals 4 x then locus of the midpoint of OA is

    Maths-General
    General
    biology

    Which one is absent in free state during origin of life ?

    Which one is absent in free state during origin of life ?

    biologyGeneral
    General
    Maths-

    Two different packs of 52 cards are shuffled together. The number of ways in which a man can be dealt 26 cards so that he does not get two cards of the same suit and same denomination is-

    Two different packs of 52 cards are shuffled together. The number of ways in which a man can be dealt 26 cards so that he does not get two cards of the same suit and same denomination is-

    Maths-General
    parallel
    General
    Maths-

    In how many ways can 6 prizes be distributed equally among 3 persons?

    In combinatorics, the rule of sum or addition principle states that it is the idea that if the complete A ways of doing something and B ways of doing something and B ways of doing something, we cannot do at the same time, then there are (A + B) ways of choosing one of the actions. In this question, there is a possibility that the student might miss considering all the cases. They may forget to consider case 2 and get a different answer.

    In how many ways can 6 prizes be distributed equally among 3 persons?

    Maths-General

    In combinatorics, the rule of sum or addition principle states that it is the idea that if the complete A ways of doing something and B ways of doing something and B ways of doing something, we cannot do at the same time, then there are (A + B) ways of choosing one of the actions. In this question, there is a possibility that the student might miss considering all the cases. They may forget to consider case 2 and get a different answer.

    General
    Maths-

    The number of ways in which mn students can be distributed equally among m sections is-

    While solving this question, the possible mistake one can make is by always choosing n students for all sections from mn students which is totally wrong because at a time one student can only be in 1 section. So, if n students are selected for 1 section then in the second section, we will choose from (mn – n).

    The number of ways in which mn students can be distributed equally among m sections is-

    Maths-General

    While solving this question, the possible mistake one can make is by always choosing n students for all sections from mn students which is totally wrong because at a time one student can only be in 1 section. So, if n students are selected for 1 section then in the second section, we will choose from (mn – n).

    General
    Maths-

    The number of ways in which 20 volunteers can be divided into groups of 4, 7 and 9 persons is-

    The number of ways in which 20 volunteers can be divided into groups of 4, 7 and 9 persons is-

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.