Question

Given the roots x=2 and x=-3, create a quadratic inStandard Form.

Answer 1

The roots of the equation are x = 2 and x = 3

The standard form of a quadratic equation is given by:

`ax^2+bx+c=0`

Step 1: Find the factors of the quadratic equation that gives x = 2 and x = 3.

`\text{ The factors are x - 2 = 0 and x - 3 = 0}`

Step 2: Multiply the factors

`\text{ (x -2)(x -3) = 0}`

Step 3: Expand the brackets.

`\begin{gathered} \text{ x(x-3)-2(x-3) = 0} \\ \text{ x}^2-3\text{x-2x+6 = 0} \\ \text{ x}^2-5\text{x + 6 = 0} \end{gathered}`

Therefore, the quadratic equation whose roots are x = 2 and x =3, written in standard form is x² - 5x + 6 = 0