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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

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

Grade:11

1 Answers

Aditya Gupta
2081 Points
4 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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