Question

What is the value of c so that x² – 11x + c is a perfect-square trinomial?

Answer 1

for a perfect square polynomial \[ax^2+bx+c =0\]
\[\Delta = b^2-4ac =0\]
apply it and get the c value

Answer 2

dont get it

Answer 3

I'll generalize my ansatz: We have got a trinomial of the following form:
\[a\cdot x² + b\cdot x + c = 0\]
Now consider the following:
\[(\sqrt{a}\cdot x + \sqrt{c})^2 = a\dot x² + 2\cdot \sqrt{a}\cdot \sqrt{c} + c\] From this follows that if your trinomial satisfies the following condition, it is a perfect square one: \[b = 2\cdot \sqrt{a}\cdot \sqrt{c}\;\Rightarrow \sqrt{c} = \frac{b}{2 \sqrt{a}}\]Now in your example, b = -11 and a = 1, so for c = 30,25 we have a perfect square trinomial.