csat-suneung 2017 Q18

csat-suneung · South-Korea · csat__math-humanities 4 marks Solving quadratics and applications Determining quadratic function from given conditions
A quadratic function $f ( x )$ with leading coefficient 1 satisfies $$\lim _ { x \rightarrow a } \frac { f ( x ) - ( x - a ) } { f ( x ) + ( x - a ) } = \frac { 3 } { 5 }$$ When the two roots of the equation $f ( x ) = 0$ are $\alpha$ and $\beta$, what is the value of $| \alpha - \beta |$? (Here, $a$ is a constant.) [4 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5 
A quadratic function $f ( x )$ with leading coefficient 1 satisfies
$$\lim _ { x \rightarrow a } \frac { f ( x ) - ( x - a ) } { f ( x ) + ( x - a ) } = \frac { 3 } { 5 }$$
When the two roots of the equation $f ( x ) = 0$ are $\alpha$ and $\beta$, what is the value of $| \alpha - \beta |$? (Here, $a$ is a constant.) [4 points]\\
(1) 1\\
(2) 2\\
(3) 3\\
(4) 4\\
(5) 5
Paper Questions
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