Quadratic equation: 3x² - 7x + 2 = 0

Mentally identify $a=3$, $b=-7$, $c=2$. Calculate $b^2=49$ and $4ac = 4 \times 3 \times 2 = 24$. Subtract $49 - 24 = 25$.

Students often forget the negative sign on $b$, but since the square of $-7$ is the same as $7^2$, it is often overlooked, or they incorrectly calculate $4 \times a \times c$ as $4 \times 3 \times 2 = 24$ vs $4 \times 3 + 2$.

The discriminant determines the nature of the roots; if $D > 0$, the roots are real and distinct, which is essential for solving inequalities involving quadratic expressions.