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Question

If the function f(x)=x2(A+2)x+Ax2, for x2 and f(2)=2, is continuous at x=2, then find the value of A.

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Solution

Here, we given that
f(x)=x2(A+2)x+Ax2
For Remainder,
Let put x=2 in x2(A+2)x+A.
as we know for continuous function remainder will be zero.
f(x)=x2(A+2)x+A
f(2)=(2)2(A+2)(2)+A
=42A4+A
A=0
So, function f(x) is written as
f(x)=x2(0+2)x+0x2
=x22xx2
=x(x2)(x2)
f(x)=x

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