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let f(x) be aquaratic eqn which is positive for all real x.then f(x)+f'(x)+f"(x)is a)>0 b)>=0 c)=0 d)

let f(x) be aquaratic eqn which is positive for all real x.then


f(x)+f'(x)+f"(x)is 


a)>0


b)>=0


c)=0


d)<0

Grade:12

1 Answers

Askiitians Expert Sahil Arora - IITD
19 Points
12 years ago

Dear Rohit

f(x)=ax2 +bx+c

since it is positive for all x

a>0 and D<0==>b2 - 4ac<0

f(x)+f'(x)+f"(x)=ax2 +bx+c+ 2ax+b+2a=ax2 +(2a+b)x+2a+b+c

D=(2a+b)2 -4a(2a+b+c)=b2-4ac-4a2 <0 and a>0

==>always positive

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Sahil Arora

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