A quadratic equation has the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants. The sum and product of the roots of a quadratic equation can be found using the following formulas: Sum of the roots, $S = \frac{-b}{a}$ Product of the roots, $P = \frac{c}{a}$ Find the sum and product of the roots of the quadratic equation $2x^2 + 5x + 3 = 0$.

Q: A quadratic equation has the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants. The sum and product of the roots of a quadratic equation can be found using the following formulas: Sum of the roots, $S = \frac{-b}{a}$ Product of the roots, $P = \frac{c}{a}$ Find the sum and product of the roots of the quadratic equation $2x^2 + 5x + 3 = 0$.

Solution Step 1: Identify the values of $a$, $b$, and $c$\nIn the given quadratic equation $2x^2 + 5x + 3 = 0$, $a = 2$, $b = 5$, and $c = 3$. Step 2: Calculate the sum of the roots\nUsing the formula $S = \frac{-b}{a}$, we can calculate the sum of the roots as $S = \frac{-5}{2}$. Step 3: Calculate the product of the roots\nUsing the formula $P = \frac{c}{a}$, we can calculate the product of the roots as $P = \frac{3}{2}$. Conclusion\nThe sum of the roots of the quadratic equation $2x^2 + 5x + 3 = 0$ is $\frac{-5}{2}$ and the product of the roots is $\frac{3}{2}$.

Question

Accepted Answer

Solution Step 1: Identify the values of $a$, $b$, and $c$
In the given quadratic equation $2x^2 + 5x + 3 = 0$, $a = 2$, $b = 5$, and $c = 3$. Step 2: Calculate the sum of the roots
Using the formula $S = \frac{-b}{a}$, we can calculate the sum of the roots as $S = \frac{-5}{2}$. Step 3: Calculate the product of the roots
Using the formula $P = \frac{c}{a}$, we can calculate the product of the roots as $P = \frac{3}{2}$. Conclusion
The sum of the roots of the quadratic equation $2x^2 + 5x + 3 = 0$ is $\frac{-5}{2}$ and the product of the roots is $\frac{3}{2}$.