If the rest of the division of f ( x ) by x³ - 3x + 5 is 3x²-2 and
the remainder of the division ( x² + f ( x ) ) ^ 2 by x³ - 3x + 5 is ax ² + bx + c ,
then a + b + c = ...
which grade question??
perhaps degree maths B Sc or M Sc level.. I am sure..
Yeah!
see answer.
Ans is -54
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The answer is the option (b) - 44...
This is certainly Degree or PG level..
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f(x) = unknown polynomial. Let g(x) = x³ - 3 x + 5
Given f Modulo g = 3 x² - 2
[x² + f ]² Modulo g
= { x⁴ + 2 x² * [f modulo g ] + [ (f modulo g)² modulo g ] } modulo g
= { x⁴ + 2 x² (3x² - 2) + [ (3x² - 2)² modulo g] } modulo g
= { 7 x⁴ - 4 x² + [ (9x⁴ - 12 x² + 4) modulo g] } modulo g
= { 16 x⁴ - 16 x² + 4 } modulo g
= 32 x² - 80 x + 4
= a x² + b x + c .... given
compare coefficients : a = 32, b = - 80 c = 4
=> a + b + c = - 44.
This is certainly Degree or PG level..
==========
f(x) = unknown polynomial. Let g(x) = x³ - 3 x + 5
Given f Modulo g = 3 x² - 2
[x² + f ]² Modulo g
= { x⁴ + 2 x² * [f modulo g ] + [ (f modulo g)² modulo g ] } modulo g
= { x⁴ + 2 x² (3x² - 2) + [ (3x² - 2)² modulo g] } modulo g
= { 7 x⁴ - 4 x² + [ (9x⁴ - 12 x² + 4) modulo g] } modulo g
= { 16 x⁴ - 16 x² + 4 } modulo g
= 32 x² - 80 x + 4
= a x² + b x + c .... given
compare coefficients : a = 32, b = - 80 c = 4
=> a + b + c = - 44.
clik on thanks... select best ans...
That is a really high level problem and you solved it so easily sir! Hats off to you! Amazing and well-formatted answer!
Ok Sir ,great :)
Similar questions
a) -34
b) -44
c) -54
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