csat-suneung 2019 Q21

csat-suneung · South-Korea · csat__math-humanities 4 marks Factor & Remainder Theorem Polynomial Construction from Root/Value Conditions

For a cubic function $f ( x )$ with leading coefficient 1 and a function $g ( x )$ that is continuous on the set of all real numbers, the following conditions are satisfied. (가) For all real numbers $x$, $f ( x ) g ( x ) = x ( x + 3 )$. (나) $g ( 0 ) = 1$ When $f ( 1 )$ is a natural number, what is the minimum value of $g ( 2 )$? [4 points]
(1) $\frac { 5 } { 13 }$
(2) $\frac { 5 } { 14 }$
(3) $\frac { 1 } { 3 }$
(4) $\frac { 5 } { 16 }$
(5) $\frac { 5 } { 17 }$

For a cubic function $f ( x )$ with leading coefficient 1 and a function $g ( x )$ that is continuous on the set of all real numbers, the following conditions are satisfied.\\
(가) For all real numbers $x$, $f ( x ) g ( x ) = x ( x + 3 )$.\\
(나) $g ( 0 ) = 1$\\
When $f ( 1 )$ is a natural number, what is the minimum value of $g ( 2 )$? [4 points]\\
(1) $\frac { 5 } { 13 }$\\
(2) $\frac { 5 } { 14 }$\\
(3) $\frac { 1 } { 3 }$\\
(4) $\frac { 5 } { 16 }$\\
(5) $\frac { 5 } { 17 }$

Paper Questions

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