Find the Sum and Product of the Roots of the Quadratic Equation 3x^2=6x+8

$3 x^{2} = 6 x + 8$

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

Move all the expressions to the left side of the equation.

Subtract $6 x$ from both sides of the equation.

$3 x^{2} - 6 x = 8$

Subtract $8$ from both sides of the equation.

$3 x^{2} - 6 x - 8 = 0$

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.

$a = 3$ , $b = - 6$ , $c = - 8$

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

Divide $6$ by $3$ .

$2$

Substitute the values into the product of roots formula $\frac{c}{a}$ .

Move the negative in front of the fraction.

$- \frac{8}{3}$

List the results.

Sum of the roots is $2$

Product of the roots is $- \frac{8}{3}$