Find the Sum and Product of the Roots of the Quadratic Equation 9/2x^2-4x+2=0

$\frac{9}{2} x^{2} - 4 x + 2 = 0$

Step 1

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

Simplify the left side.

Combine $\frac{9}{2}$ and $x^{2}$ .

$\frac{9 x^{2}}{2} - 4 x + 2 = 0$

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.

$a = \frac{9}{2}$ , $b = - 4$ , $c = 2$

Step 2

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

Multiply the numerator by the reciprocal of the denominator.

$4 (\frac{2}{9})$

Multiply $4 (\frac{2}{9})$ .

Combine $4$ and $\frac{2}{9}$ .

$\frac{4 \cdot 2}{9}$

Multiply $4$ by $2$ .

$\frac{8}{9}$

Step 3

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

Multiply the numerator by the reciprocal of the denominator.

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

Multiply $2 (\frac{2}{9})$ .

Combine $2$ and $\frac{2}{9}$ .

$\frac{2 \cdot 2}{9}$

Multiply $2$ by $2$ .

$\frac{4}{9}$

Step 4

List the results.

Sum of the roots is $\frac{8}{9}$

Product of the roots is $\frac{4}{9}$