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Q.

Let f be a continuous function defined on [–2013, 2013] such that f(x) is irrational for each x[2013,2013] and f(0)=2+3+5 The equation f(2013)x2+2f(0)x+f(2013)=0 has

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a

only rational roots

b

only irrational roots

c

one rational and one irrational root

d

imaginary roots

answer is A.

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Detailed Solution

f(x) takes is rational, x
(x) is a constant function.
f(x)=2+3+5,xf(2013)x2+2f(0)x+f(2013)=0 (2+3+5)x2+2x+1=0x=1
It has only rational roots

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