Chapter 8.7, Problem 49HP

To determine

To write a perfect square trinomial equation in which the coefficient of the middle term is negative and the last term is a fraction.

Answer to Problem 49HP

  $x^2-\frac{3}{2}x+\frac{9}{16}$

Explanation of Solution

Given:

The coefficient of middle term is negative and the last term is a fraction.

Calculation:

Consider the equation which is a perfect square trinomial.

  $\Rightarrow x^2-\frac{3}{2}x+\frac{9}{16}$

Here the middle term is negative and the last term is a fraction.

Now, solve the equation.

  $\begin{array}{l}\Rightarrow x^2-\frac{3}{2}x+\frac{9}{16}\\ $ \Rightarrow x^2-2\times \frac{3}{4}x+{(\frac{3}{4})}^2$$ \Rightarrow {(x-\frac{3}{4})}^2$\end{array}$

The factor of the equation is ${(x-\frac{3}{4})}^2.$

Therefore, $x=\frac{3}{4}.$

Conclusion:

Thus, the perfect square trinomial is $x^2-\frac{3}{2}x+\frac{9}{16}.$