Find the Sum and Product of the Roots of the Quadratic Equation 9x^2-6x=8

$9 x^{2} - 6 x = 8$

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

Subtract $8$ from both sides of the equation.

$9 x^{2} - 6 x - 8 = 0$

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.

$a = 9$ , $b = - 6$ , $c = - 8$

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

Cancel the common factor of $6$ and $9$ .

Factor $3$ out of $6$ .

$\frac{3 (2)}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2}{3}$

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

Move the negative in front of the fraction.

$- \frac{8}{9}$

List the results.

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

Product of the roots is $- \frac{8}{9}$