taiwan-gsat 2025 Q6

taiwan-gsat · Other · gsat__math-b 5 marks Polynomial Division & Manipulation

Let $a , b , c$ be real numbers, and the polynomial $f ( x ) = a ( x - 1 ) ( x - 3 ) + b ( x - 1 ) ( x - 4 ) + c ( x - 3 ) ( x - 4 )$ simplifies to $f ( x ) = x ^ { 2 }$ . Regarding the magnitude relationship of $a , b , c$, select the correct option.
(1) $a > b > c$
(2) $a > c > b$
(3) $b > c > a$
(4) $c > a > b$
(5) $c > b > a$

Let $a , b , c$ be real numbers, and the polynomial $f ( x ) = a ( x - 1 ) ( x - 3 ) + b ( x - 1 ) ( x - 4 ) + c ( x - 3 ) ( x - 4 )$ simplifies to $f ( x ) = x ^ { 2 }$ . Regarding the magnitude relationship of $a , b , c$, select the correct option.\\
(1) $a > b > c$\\
(2) $a > c > b$\\
(3) $b > c > a$\\
(4) $c > a > b$\\
(5) $c > b > a$

Paper Questions

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