Question

the coefficient $b$ in the trinomial formula must be ______ the product of the square roots of $a$ and $c$.

Explanation:

A perfect square trinomial has the form $a^2 + 2ab + b^2$ or $a^2 - 2ab + b^2$. For a general trinomial $ax^2 + bx + c$ that is a perfect square, $b = \pm 2\sqrt{a}\sqrt{c}$, meaning $b$ must be twice the product of the square roots of $a$ and $c$.

Answer:

twice