Question 26

A function $$f(x) = ax^2 + bx + c$$, where $$a, b, c \in R$$, satisfies the property $$f(x) < x$$ for all $$x \in R$$. Then which of the following statements must always be TRUE ?

Solution

$$f(x) = ax^2 + bx + c$$ < x

$$ax^2+x\left(b-1\right)+c\ <0$$

Hence discriminant < 0 and $$a\le\ 0$$

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