Find the Sum and Product of the Roots of the Quadratic Equation 4x^2+6x+3=0

$4 x^{2} + 6 x + 3 = 0$

Step 1

Find $a$ , $b$ , and $c$ .

Once the quadratic is in standard form, the values of $a$ , $b$ , and $c$ can be found.

$a x^{2} + b x + c$

Use the standard form of the equation to find $a$ , $b$ , and $c$ for this quadratic.

$a = 4$ , $b = 6$ , $c = 3$

Step 2

Substitute the values into the sum of roots formula $- \frac{b}{a}$ .

Cancel the common factor of $- 6$ and $4$ .

Factor $2$ out of $- 6$ .

$\frac{2 (- 3)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 \cdot - 3}{2 \cdot 2}$

Cancel the common factor.

$\frac{2 \cdot - 3}{2 \cdot 2}$

Rewrite the expression.

$\frac{- 3}{2}$

Move the negative in front of the fraction.

$- \frac{3}{2}$

Step 3

List the results.

Sum of the roots is $- \frac{3}{2}$

Product of the roots is $\frac{3}{4}$