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Math·Advanced Math·Nonlinear functions

hard

$f(x)=(x-a)(x-b)$ The function $f$ is defined by the given equation, where $a$ and $b$ are integer constants. If $f(39)>0$, $f(42)<0$, and $f(45)>0$, which of the following could be the value of $a+b$?

A

$42$

B

$44$

C

$81$

D

$83$