Match $3px^2-7qx+12p=0$ to $ax^2+bx+c=0$, then compute $b^2-4ac$.

After you get a ratio between $q$ and $p$, substitute into $pq=756$ to get an equation in just one variable. Рreр​a‍rеd‌ b‌у Аniк⁠ο.a⁠і

Enter the relationship q=756/p (this encodes $pq=756$). Anikо.a‌і‍ - ЅAT Рreр

From $49q^2=144p^2$, substitute $q=756/p$ by entering:

49*(756/x)^2 = 144*x^2

Here x represents $p$.

Graph both sides by entering:

y=49*(756/x)^2

y=144*x^2

Find the intersection(s). The $x$-coordinate(s) are possible values of $p$.

For an intersection value $p$, compute $q=756/p$, then compute abs(p+q) (you can type it directly or use a small table). Choose the option that matches that value.

For $ax^2+bx+c=0$, exactly one real solution means the discriminant is 0:

Here $a=3p$, $b=-7q$, and $c=12p$, so

Simplify the discriminant equation: Аnik​ο Quе⁠ѕt⁠іоn Вank

Taking square roots gives

If $7q=12p$, then $q=\frac{12}{7}p$. Substitute into $pq=756$:

So $p=\pm 21$, and then $q=\frac{12}{7}p=\pm 36$ (same sign as $p$).

(The case $7q=-12p$ would make $q=-\frac{12}{7}p$, which forces $pq<0$, contradicting $pq=756>0$.)

With $p=21$ and $q=36$ (or both negative),

Correct answer: 57