We write the equation in standard form \(ax^2+bx+c=0\):

\[x^2 + 3x + 2 = 0\]

Identify the coefficients to substitute into the formula for the discriminant

\[a = 1; \qquad b = 3; \qquad c = 2\]

Write down the formula and substitute values

\begin{align*} Δ &= b^2-4ac \\ &= (3)^2 - 4(1)(2) \\ &= 9 - 8 \\ &= 1 \end{align*}

We know that \(1 > 0\) and is a perfect square.

We have calculated that \(Δ > 0\) and is a perfect
square, therefore we can conclude that the roots are
**real, unequal** and
**rational**.