Question

the form of a perfect square trinomial is $ax^2 + bx + c$, where $a$ and $c$ must be __________ .

Explanation:

In a perfect square trinomial \(ax^2 + bx + c\), it can be written as \((\sqrt{a}x \pm \sqrt{c})^2\). For \(\sqrt{a}\) and \(\sqrt{c}\) to be real numbers (and for the trinomial to factor into a squared binomial of real terms), \(a\) and \(c\) must be perfect squares (positive values that are the square of some real number; they can also be described as non-negative real numbers where their square roots are real, but the key defining trait is that they are perfect squares to fit the perfect square trinomial form).

Answer:

Perfect squares (positive real numbers that are squares of real numbers)