Chapter 9, Problem 11STP

a)

To determine

To find: the factors of $x^2-7x+10$ .

Answer to Problem 11STP

The factors of

  $x^2-7x+10$ are $\left(x-2\right)\left(x-5\right)$ .

Explanation of Solution

Given:

Graph is given as,

Quadratic function is given as,

  $x^2-7x+10$

So,

  $\begin{array}{l}{x}^2-7x+10=x^2-5x-2x+10\\ x^2-5x-2x+10=x\left(x-5\right)-2\left(x-5\right)\\ x\left(x-5\right)-2\left(x-5\right)=\left(x-2\right)\left(x-5\right)\end{array}$

So,

The factors of

  $x^2-7x+10$ are $\left(x-2\right)\left(x-5\right)$ .

b)

To determine

To find: the solutions of $x^2-7x+10=0$ .

Answer to Problem 11STP

The solutions of

  $x^2-7x+10=0$ are $x=2,5$ .

Explanation of Solution

Given:

Graph is given as,

Quadratic equation is given as,

  $x^2-7x+10=0$

So,

  $\begin{array}{l}{x}^2-7x+10=0\\ x^2-5x-2x+10=0\\ x\left(x-5\right)-2\left(x-5\right)=0\\ \left(x-2\right)\left(x-5\right)=0\\ x=2,5\end{array}$

So,

The solutions of

  $x^2-7x+10=0$ are $x=2,5$ .

c)

To determine

To find: the points where the graph crosses the x -axis and comparing these values to the solutions of

  $x^2-7x+10=0$

Explanation of Solution

Given:

Graph is given as,

It can be seen that graph crosses x -axis at x = 2 and x = 5 and the solutions of given quadratic equation is also x = 2 and x = 5 which suggests that the points at which graph crosses the x -axis are the solutions of the quadratic equation.