ICSE Class X Math 2015 Solved Paper

Question : 30

Total: 52

Find ' a ' if the two polynomials ax3+3x2−9 and 2x3+4x+a, leaves the same remainder when divided by x+3.

Solution:

Let f(x)‌=ax3+3x2−9
and g(x)‌=2x3+4x+a
putting x+3‌=0
x‌=−3
Since remainder is same
f(−3)‌=g(−3)
a(−3)3+3(−3)2−9‌ =2(−3)3+4(−3)+a
−27a+27−9‌=−54−12+a
27a+a‌=27−9+54+12
28a‌=84
a‌=3

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