Chapter 12, Problem 9CR

To determine

To define: The best method for solving the equation $2y^2+8y=0$ and the options are,

  $\text{a}\text{.}$ Factoring

  $\text{b}\text{.}$ Property of square roots of equal numbers

  $\text{c}\text{.}$ Completing the square

  $\text{d}\text{.}$ Quadratic formula

Answer to Problem 9CR

The $\text{a}\text{.}$ Factoring option is true as best method of solving the equation $2y^2+8y=0$ .

Explanation of Solution

Given information:

The provided equation,

  $2y^2+8y=0$

And the provided options are,

  $\text{a}\text{.}$ Factoring

  $\text{b}\text{.}$ Property of square roots of equal numbers

  $\text{c}\text{.}$ Completing the square

  $\text{d}\text{.}$ Quadratic formula

Methods for solving a Quadratic equation,

If the equation is in this form $a{x}^2+bx+c=0$ then use quadratic method.

If the equation is in this form $a{x}^2+bx=0$ then use Factoring method.

If the equation is in this form $a{x}^2+c=0$ then use property of square roots of equal numbers.

If the equation is in this form $x^2+bx+c=0$ and $\text{b}$ is an even number then use Completing the square method.

Since, the provided equation $2y^2+8y=0$ is in the form $a{x}^2+bx=0$ so, using the Factoring method as,

  $2y^2+8y=0$

In equation $2y$ is common so take common $2y$ as,

  $2y\left(y+4\right)=0$

Furthermore,

  $2y=0\text{or}y+4=0$

Therefore,

  $y=0\text{or}y=-4$

The best method for solving $2y^2+8y=0$ is factoring.

So, the $\text{a}\text{.}$ Factoring option is true.