csat-suneung· South-Korea· csat__math-science3 marks
A quartic function $f ( x )$ with positive leading coefficient satisfies the following conditions. $f ^ { \prime } ( x ) = 0$ has three distinct real roots $\alpha , \beta , \gamma ( \alpha < \beta < \gamma )$, and $f ( \alpha ) f ( \beta ) f ( \gamma ) < 0$. Which of the following in are correct? [3 points] ㄱ. The function $f ( x )$ has a local maximum value at $x = \beta$. ㄴ. The equation $f ( x ) = 0$ has two distinct real roots. ㄷ. If $f ( \alpha ) > 0$, then the equation $f ( x ) = 0$ has a real root less than $\beta$. (1) ᄀ (2) ᄃ (3) ᄀ, ᄂ (4) ㄴ,ㄷ (5) ᄀ, ᄂ, ᄃ
A quartic function $f ( x )$ with positive leading coefficient satisfies the following conditions.\\
$f ^ { \prime } ( x ) = 0$ has three distinct real roots $\alpha , \beta , \gamma ( \alpha < \beta < \gamma )$, and $f ( \alpha ) f ( \beta ) f ( \gamma ) < 0$.\\
Which of the following in <Remarks> are correct? [3 points]
\textbf{<Remarks>}\\
ㄱ. The function $f ( x )$ has a local maximum value at $x = \beta$.\\
ㄴ. The equation $f ( x ) = 0$ has two distinct real roots.\\
ㄷ. If $f ( \alpha ) > 0$, then the equation $f ( x ) = 0$ has a real root less than $\beta$.\\
(1) ᄀ\\
(2) ᄃ\\
(3) ᄀ, ᄂ\\
(4) ㄴ,ㄷ\\
(5) ᄀ, ᄂ, ᄃ