Chapter 9, Problem 14PT

To determine

To solve equation by factoring.

Answer to Problem 14PT

  $x=-2,20$

Explanation of Solution

Given information :

The function provided is $5x^2-31x+6=0$

Formula used :

For some of the equations the solution can be found by factoring. If the factored form of a quadratic equation has real numbers, it will have roots.

  $(x-h)(x-k)=0$

In the factored form it is assumed that at least one of the factors is equal to 0. Therefore, if product if two factors is 0 then at least one of the factors must be zero, this is known as the Zero Product Property

Either,

  $(x-h)=0$

Or,

  $(x-k)=0$

Calculation :

  $5x^2-31x+6=0$

The above expression can also be written as.

  $5x^2-30x-x+6=0$

In factored form.

  $(5x-1)(x-6)=0$

Either,

  $5x-1=0$

Or,

  $x-6=0$

The above expression can be solved to get $x=0.2,6$

We get two roots $x=0.2,6$ , as $5x^2-31x+6=0$ is a not perfect square.