Question
Question: Let f(x) be a quadratic expression which is positive for all real values of x, then for all real x, ...
Let f(x) be a quadratic expression which is positive for all real values of x, then for all real x, 10 [f(x) + f (– x)] is
A
> 0
B
³ 0
C
< 0
D
£ 0
Answer
> 0
Explanation
Solution
Let f(x) = ax2 + bx + c
Since f(x) is + ve for all real values of x
\ a, b, c > 0 f (– x) = ax2 – bx + c
\ f(x) + f(– x) = 2 (ax2 + c) > 0
\ 10 [f(x) + f(– x)] > 0