Question

find a real number c such that the algebraic expression is a perfect square trinomial.

9t^2-12t+c

Answer 1

An applicable perfect square is of the form: \[(at+b)^2=a^2t^2+2abt+c\] Thus \[a^2=9, \text{ }2ab=-12, \text{ }b^2=c\] Therefore: \[a=\pm 3\] Thus: \[b = \dfrac{-12}{2a} = \dfrac{-12}{2(\pm 3)}=\pm 2\] Therefore: \[c=b^2 = \left(\pm 2\right)^2=4\]