Question

Find the roots for the quadratic equation using factoring
`x ^(2) = 3x - 2`

Answer 1

The roots of the quadratic equation are x= 1 or x = 2

Here, we want to find the roots of the quadratic equation

We are going to use the factoring method to do this

Firstly, we will make all the terms equal to zero

We can proceed by rewriting the equation as follows;

`x^2-3x+2\text{ = 0}`

We then move on to factor from here

We will need two factors which when added give -3x and when multiplied will give 2x^2

Thus, we can have the equation above written as follows;

`\begin{gathered} x^2-2x-x+2=\text{ 0} \\ \\ x(x-2)-1(x-2)\text{ = 0} \\ (x-1)(x-2)\text{ = 0} \\ x-1\text{ = 0 or x-2 = 0} \\ x\text{ = 1 or x = 2} \end{gathered}`

Thus, the roots of the quadratic equation are x = 1 or 2