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Grade 11Differential Calculus

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

7 Years agoGrade 11

1 Answer

Aditya Gupta

Approved Tutor Answer7 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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