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If $2,3,6$ are the roots of the polynomial $f(x)=x^3+a x^2+b x+c$, where $a, b, c, \in C$.
Then, the value of $a-c$ is
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Then, the value of $a-c$ is
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The correct answer is:
$25$
$\begin{array}{rlrl} & & x^3+a x^2+b x+c=(x-2)(x-3)(x-6) \\ \Rightarrow & & \quad x^3+a x^2+b x+c \\ & = & x^3-11 x^2+36 x-36 \\ & \Rightarrow & a & =-11, b=36, c=-36 \\ \therefore & a-c & =-11+36=25\end{array}$
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