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If f(X) is a quadratic expression which is positive for all real X,if g(X)=f(X)+f'(X)+f(X),then which one is correct,(A)g(X)(B)g(X)>0(C)g(X)=0(D)g(X)>=0

Alshat porwal , 6 Years ago
Grade 11
anser 1 Answers
Aditya Gupta

Last Activity: 6 Years ago

let f(x)= ax^2+bx+c, where b^2 – 4ac
now, g(x)= ax^2+(b+2a)x+2a+b+c
discriminant of g(x) turns out to be
(b+2a)^2 – 4a(2a+b+c)= b^2 – 4ac – 4a^2, which is always less than zero provided b^2 – 4ac
so, g(x) is always greater than zer0
option B is correct

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