If l, m (l

Question

(C) Let $f(x) = ax^2 + bx + c$. Since $l$ and $m$ are roots,$f(x) = a(x-l)(x-m)$.If $\alpha \in (l, m)$,then $(x-l)$ and $(x-m)$ have opposite signs,s

Vedclass · Accepted Answer

$\frac{-|a|}{a}$,when $\alpha \in (l, m)$

Vedclass · Answer

(C) Let $f(x) = ax^2 + bx + c$. Since $l$ and $m$ are roots,$f(x) = a(x-l)(x-m)$.If $\alpha \in (l, m)$,then $(x-l)$ and $(x-m)$ have opposite signs,so $f(x)$ has the opposite sign of $a$.Thus,if $a > 0$,$f(x)  0$.In both cases,$\frac{|f(x)|}{f(x)} = -1$ for $x \in (l, m)$.Since $\frac{|a|}{a} = 1$ if $a > 0$ and $-1$ if $a  0$ and $1$ when $a Wait,if $a > 0$,$\frac{-|a|}{a} = -1$. If $a Therefore,$\lim_{x \rightarrow \alpha} \frac{|f(x)|}{f(x)} = \frac{-|a|}{a}$ when $\alpha \in (l, m)$.

If $l, m$ $(l < m)$ are roots of $ax^2 + bx + c = 0$,then $\lim_{x \rightarrow \alpha} \frac{|ax^2 + bx + c|}{ax^2 + bx + c} = $

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