Given is the expression, x² + 12x + n
It says to find value of 'n' that converts it into a Perfect Square Trinomial.
A perfect square trinomial is a quadratic expression which has a single root with multiplicity 2. i.e. it is of the form :- x² + 2bx + b² = (x + b)²
On comparing it with the given expression, we get :-
So 2b = 12 and n = b²
b = 6
and so b² = 6² = 36.
⇒ n = 36
Hence, x² + 12x + 36 = (x + 6)² i.e. n = 36 is the final answer.
