Find the equation whose sum of root and product of root is 2 and 3

For a quadratic equation of the form $ax^2 + bx + c = 0$, the sum of the roots is $\alpha + \beta = -\frac{b}{a}$ and the product of the roots is $\alpha \beta = \frac{c}{a}$.
We can also consider a monic quadratic equation (where $a=1$), which is $x^2 - (\alpha + \beta)x + \alpha \beta = 0$.

The problem states that the sum of the roots is 2, so $\alpha + \beta = 2$.
The problem states that the product of the roots is 3, so $\alpha \beta = 3$.

Using the formula $x^2 - (\alpha + \beta)x + \alpha \beta = 0$, we substitute the values from Step 2.
$x^2 - (2)x + 3 = 0$

The equation is $x^2 - 2x + 3 = 0$.

x^2 - 2x + 3 = 0