Chapter 8.7, Problem 60PFA

To determine

To find: Whether given statement is true or false.

Answer to Problem 60PFA

False

Explanation of Solution

Given information:

For a trinomial to be perfect square trinomial, the middle term must be positive.

Given

For a trinomial to be perfect square trinomial, the middle term must be positive.

Given statement if False.

Counter example is

  $9x^2-12x+4$

  $\begin{array}{l}9x^2-12x+4=9x^2-6x-6x+4\\ \Rightarrow 9x^2-12x+4=3x\left(3x-2\right)-2\left(3x-2\right)\\ \Rightarrow 9x^2-12x+4=\left(3x-2\right)\left(3x-2\right)\\ \Rightarrow 9x^2-12x+4={\left(3x-2\right)}^2\end{array}$

Here

  $9x^2-12x+4={\left(3x-2\right)}^2$

Is a perfect square and middle term is not positive

So, given statement is False.