Maths-
General
Easy

Question

The polynomials a x to the power of 3 end exponent plus 3 x to the power of 2 end exponent minus 3 and 2 x to the power of 3 end exponent minus 5 x plus a when divided by left parenthesis x minus 4 right parenthesis leaves remainders R subscript 1 end subscript and R subscript 2 end subscript respectively then value of stack stack a with _ below with _ below if 2 R subscript 1 end subscript minus R subscript 2 end subscript equals 0

  1. negative fraction numerator 18 over denominator 127 end fraction    
  2. fraction numerator 18 over denominator 127 end fraction    
  3. fraction numerator 17 over denominator 127 end fraction    
  4. negative fraction numerator 17 over denominator 127 end fraction    

The correct answer is: negative fraction numerator 18 over denominator 127 end fraction


    In the question two polynomials are given and asked to find the difference in their remainder if divided by x-4
    x minus 4 right parenthesis 2 x cubed minus 5 x plus a left parenthesis 2 x squared plus 8 x plus 27
space space space space space space space space space 2 x cubed minus 8 x squared
long dash long dash long dash long dash long dash long dash long dash long dash
space space space space space space space space 8 x squared minus 5 x plus a
space space space space space space space space 8 x squared minus 32 x
long dash long dash long dash long dash long dash long dash long dash long dash
space space space space space space space 27 x plus a
space space space space space space space 27 x minus 108
long dash long dash long dash long dash long dash long dash long dash long dash
R 2 equals 108 plus a
N o w space f o r space R 1
x minus 4 right parenthesis a x cubed plus 3 x squared minus 3 left parenthesis a x squared plus left parenthesis 3 plus 4 a right parenthesis x plus 4 left parenthesis 3 plus 4 a right parenthesis
space space space space space space space space space space a x cubed minus 4 a x squared
long dash long dash long dash long dash long dash long dash long dash long dash
space space space space space space space space space 3 x squared plus 4 a x squared minus 3
space space space space space space space space space space 3 x squared plus 4 a x squared minus 4 left parenthesis 3 plus 4 a right parenthesis x
minus negative negative negative negative negative negative negative negative negative negative negative negative negative
space space space space space space space space space space 4 left parenthesis 3 plus 4 a right parenthesis x minus 3
space space space space space space space space space 4 left parenthesis 3 plus 4 a right parenthesis x minus 16 left parenthesis 3 plus 4 a right parenthesis
minus negative negative negative negative negative negative negative negative negative negative negative negative negative
R 1 equals negative 3 plus 16 left parenthesis 3 plus 4 a right parenthesis
B y space s o l v i n g space t h e space g i v e n space e q u a t i o n space 2 R 1 minus R 2 equals 0
w e space g e t space a
H e n c e space a equals negative 18 over 127


space space space space space space space space space space

space space space space space space space

space space space space space space space space space space

    a=-18/127

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