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UPSC NDA II 2014 Mathematics Paper

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For the next three (03) items that follow:

Let

f(x)=ax^2+bx+c

such that

f(1)=f(-1)

and a,b,c are in Arithmetic Progression

[NDA II 2014]

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Question : 89 of 120

Marks: +1, -0

f'(a),f'(b),f'(c)

A.P
G.P
H.P
Arithmetico-geometric progression

Solution:

f'(x)=2ax+b

\Rightarrow f'(a)=2a^2+b

\Rightarrow f'(b)=2ab+b

\Rightarrow f'(c)=2ac+b

f'(a)+f'(c)=2a(a+c)+2b=4ab+2b=2f'(b)

f'(a),f'(b)

and

f'(c)

are in A.P

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