Chapter 8, Problem 7SGR

To determine

To state if the statement is true or false.

Answer to Problem 7SGR

true.

Explanation of Solution

Given:

Statement: $x^2-12x+36$ is an example of perfect square trinomial.

Concept used:

Factorisation using perfect square trinomial method.

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

Consider the given expression,

  $x^2-12x+36$

Substituting in the formula for $a=1,b=-12,c=36$

  $\begin{array}{l}x=\frac{-(-12)\pm \sqrt{{(-12)}^2-4(1)(36)}}{2(1)}\\ x=\frac{12\pm \sqrt{144-144}}{2}\\ x=\frac{12}{2}=6\end{array}$

Thus, the roots are,

  $x_1=x_2=6$

Therefore, the expression can be factored as,

  $\Rightarrow x^2-12x+36=(x-6)(x-6)$

Conclusion:

Therefore, $x^2-12x+36$ is an example of perfect square trinomial.