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ICSE Class X Math 2015 Paper

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Question : 30 of 52
Marks: +1, -0
Find ' aa ' if the two polynomials ax3+3x2−9a x^3+3 x^2-9 and 2x3+4x+a2 x^3+4 x+a, leaves the same remainder when divided by x+3x+3.
Solution:  
Let f(x)  =ax3+3x2−9f(x)\;=a x^3+3 x^2-9
and g(x)  =2x3+4x+ag(x)\;=2 x^3+4 x+a
putting x+3  =0x+3\;=0
x  =−3x\;=-3
Since remainder is same
f(−3)  =g(−3)f(-3)\;=g(-3)
a(−3)3+3(−3)2−9  a(-3)^3+3(-3)^2-9\; =2(−3)3+4(−3)+a=2(-3)^3+4(-3)+a
−27a+27−9  =−54−12+a-27 a+27-9\;=-54-12+a
27a+a  =27−9+54+1227 a+a\;=27-9+54+12
28a  =8428 a\;=84
a  =3a\;=3
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