1. Let's start by stating the problem: We want to find the sum and product of the roots of a quadratic equation. 2. A quadratic equation is generally written as $$ax^2 + bx + c = 0$$ where $a \neq 0$. 3. The roots of this quadratic equation are the values of $x$ that satisfy the equation. 4. The sum and product of the roots can be found using the coefficients $a$, $b$, and $c$ without solving the equation explicitly. 5. The formulas are: - Sum of roots: $$\alpha + \beta = -\frac{b}{a}$$ - Product of roots: $$\alpha \times \beta = \frac{c}{a}$$ 6. These come from Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots. 7. For example, if the quadratic is $$2x^2 - 4x + 3 = 0$$, then: - Sum of roots: $$-\frac{-4}{2} = 2$$ - Product of roots: $$\frac{3}{2} = 1.5$$ 8. This means the two roots add up to 2 and multiply to 1.5. 9. This method is very useful because it avoids solving the quadratic equation directly and gives quick insight into the roots. Final answer: - Sum of roots = $$-\frac{b}{a}$$ - Product of roots = $$\frac{c}{a}$$