ICSE Class X Math 2015 Solved Paper

Question : 30 of 52

Marks: +1, -0

Find '

a

' if the two polynomials

a x^3+3 x^2-9

and

2 x^3+4 x+a

, leaves the same remainder when divided by

x+3

Solution:

Let

f(x)\;=a x^3+3 x^2-9

and

g(x)\;=2 x^3+4 x+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

-27 a+27-9\;=-54-12+a

27 a+a\;=27-9+54+12

28 a\;=84

a\;=3

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