If the polynomials 2xcube ax2 3x-5 and xcube +x2 -4x+a leave the same reamainder when divided byx-2 find a
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x-2=0
x= 2
f(x) = 2x^3 +ax^2 +3x-5
=> f(2) = 2(2)^3 + a(2)^2 +3(2) -5.
= 2*8 + a(4) +6 -5
= 16 + 4a +6-5
= 16 + 6 - 5 + 4a
=> 4a = -17
___________(i)
f(x)= x^3 +x^2 -4x +a
=> f(2)= 2^3 + 2^2 -4(2) +a
= 8+4- 8 + a
= 12- 8 +a
=> a= 4
__________(ii)
from (i) and (ii)
4a+a = -17 + 4
=> 5a = -13
=> a = -13/5
x= 2
f(x) = 2x^3 +ax^2 +3x-5
=> f(2) = 2(2)^3 + a(2)^2 +3(2) -5.
= 2*8 + a(4) +6 -5
= 16 + 4a +6-5
= 16 + 6 - 5 + 4a
=> 4a = -17
___________(i)
f(x)= x^3 +x^2 -4x +a
=> f(2)= 2^3 + 2^2 -4(2) +a
= 8+4- 8 + a
= 12- 8 +a
=> a= 4
__________(ii)
from (i) and (ii)
4a+a = -17 + 4
=> 5a = -13
=> a = -13/5
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