SAT Math Practice Question #25128 - SATify | SATify

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SAT Math Practice Question #25128 - SATify | SATify

#25128

algebra

polynomials

hard

150 sec

Let $a$ and $b$ be the roots of the equation $x^{2} - m x + 3 = 0$ . Suppose that $a + \frac{1}{b}$ and $b + \frac{1}{a}$ are the roots of the equation $x^{2} - p x + q = 0$ . What is $q$ ?

A.

$\frac{13}{3}$

B.

$\frac{14}{3}$

C.

$5$

D.

$\frac{16}{3}$

E.

$\frac{17}{3}$