Solve the problem.
-Find all values of $b$ that will make the polynomial a perfect square trinomial. $25 x ^ { 2 } + 40 x + b$
A) 80
B) 4
C) 16
D) $4 , - 4$

Question

Quizplus · Accepted Answer

For a trinomial $ax^2 + bx + c$ to be a perfect square, it must be of the form $(\sqrt{a}x + \sqrt{c})^2$. Given $25x^2 + 40x + b$, comparing it to $a=25$ (so, $\sqrt{a} = 5$) and $b=40$, we find $c$ by using the relationship in a perfect square trinomial: $b = 2\sqrt{a}\sqrt{c}$. Solving $40 = 2*5*\sqrt{c}$ gives $\sqrt{c} = 4$, so $c = 16$.

Solve the Problem bbb That Will Make the Polynomial a Perfect Square Trinomial

Solve the Problem $b$ That Will Make the Polynomial a Perfect Square Trinomial