Find the Sum and Product of the Roots of the Quadratic Equation 4x^2+3x-5=0

$4 x^{2} + 3 x - 5 = 0$

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.

$a = 4$ , $b = 3$ , $c = - 5$

Step 2

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

Move the negative in front of the fraction.

$- \frac{3}{4}$

Step 3

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

Move the negative in front of the fraction.

$- \frac{5}{4}$

Step 4

List the results.

Sum of the roots is $- \frac{3}{4}$

Product of the roots is $- \frac{5}{4}$