1. The problem is to find the discriminant of a quadratic equation and determine how many solutions it has. 2. The discriminant $\Delta$ of a quadratic equation $ax^2 + bx + c = 0$ is given by the formula: $$\Delta = b^2 - 4ac$$ 3. The discriminant tells us the nature of the roots: - If $\Delta > 0$, there are 2 distinct real roots. - If $\Delta = 0$, there is exactly 1 real root (a repeated root). - If $\Delta < 0$, there are no real roots, but 2 complex roots. 4. To solve for the discriminant, identify $a$, $b$, and $c$ from the quadratic equation and substitute into the formula. 5. Example: For $2x^2 + 3x - 2 = 0$, $a=2$, $b=3$, $c=-2$. 6. Calculate: $$\Delta = 3^2 - 4 \times 2 \times (-2) = 9 + 16 = 25$$ 7. Since $\Delta = 25 > 0$, the equation has 2 distinct real roots. This method applies to any quadratic equation to find the discriminant and number of solutions.