Chapter ISG, Problem 9.5.4P

(a)

To determine

To find: The possible equation whose one root between 4 and 5.

Answer to Problem 9.5.4P

  $y=x^2-4x-1$

Explanation of Solution

Given: Jeremy writes a trinomial that can be solved by completing the square and cannot be solved by factoring. One of the solutions of this equation is between 4 and 5.

Let one root between 4 and 5 be 4.5.

So, the possible equation is $y=x^2-4x-1$

(b)

To determine

To find: The possible solution of the equation using completing square.

Answer to Problem 9.5.4P

  $2+\sqrt{5}\text{ and }2-\sqrt{5}$

Explanation of Solution

Given: Jeremy writes a trinomial that can be solved by completing the square and cannot be solved by factoring. One of the solutions of this equation is between 4 and 5.

Let one root between 4 and 5 be 4.5.

So, the possible equation is $y=x^2-4x-1$

  $\begin{array}{c}{x}^2-4x-1=0\\ x^2-4x+4=1+4\\ {\left(x-2\right)}^2=5\\ x-2=\pm \sqrt{5}\\ x=2\pm \sqrt{5}\end{array}$

Hence, the solutions of the equation are $2+\sqrt{5}\text{ and }2-\sqrt{5}$

(c)

To determine

To find: The possible solution of the equation using completing square.

Answer to Problem 9.5.4P

Prime equation

Explanation of Solution

Given: Jeremy writes a trinomial that can be solved by completing the square and cannot be solved by factoring. One of the solutions of this equation is between 4 and 5.

Let one root between 4 and 5 be 4.5.

So, the possible equation is $y=x^2-4x-1$

This is prime equation so can’t factor it. To solve prime equation using completing square.