Chapter 4.5, Problem 7LC

Solution

To Compare and Contrast: The easier way to solve a quadratic equation by factoring than to solve it using a table.

The easier way to solve a quadratic equation is by factoring because it is time consumption and need of no tables.

Given:

Compare and Contrast the easy way to solve a quadratic equation by factoring than to solve it

using a table.

Explanation:

Two types of methods to solve the equation:

• Solving quadratic equation by factoring
• Solving quadratic equation with table.

Compare:

When compare factoring method with table method factoring method needs no lengthy

calculations need no tables and also time consumption.

The first method can be used only for certain kinds of quadratic equations, but the second method can be used for any kind of quadratic equation.

To solve a quadratic equation using the first method, it must have the following features.

In the first method, the quadratic equation can be factored easily.

Factoring quadratic equations is easy if their coefficients are integers and have recognizable factoring patterns.

Example: $x^2-3x+2=0$

The coefficients are $1,-3$ and $2$ :

This equation also contains the factoring pattern $-1-2=-3$ and $\left(-1\right)\left(-2\right)=2$

Thus, the equation factored as:

  $\begin{array}{c}{x}^2-3x+2=0\\ x^2-2x-x+2=0\\ x\left(x-2\right)-1\left(x-2\right)=0\\ \left(x-1\right)\left(x-2\right)=0\end{array}$

Non- example: $x^2-x+3=0$

Despite having integer coefficients $1,-1,$ and $3$ , this equation does not contain the factoring pattern. Therefore, only tables can be used to factorize it.