How do you determine the sum and product of the roots of #3x^2 + 2x = 0#?

Question

Savannah Anderson · Accepted Answer

Sum of the roots = #-2/3# and product 0. Make the coefficient of #x^2# as 1  by dividing the equation  by 3.
#x^2# + #2/3# x +0=0 The negative of the coefficient of x, gives the sum of the roots, and the constant term 0, gives the product of the roots of the quadratic equation.

Nathan Axel · Answer

undefined To determine the sum and product of the roots of $3x^2 + 2x = 0$, first, identify the coefficients of the quadratic equation, $a$, $b$, and $c$. In this equation, $a = 3$, $b = 2$, and $c = 0$. Then, use the formulas for sum and product of roots, which are given by:

Sum of roots, $S = -\frac{b}{a}$

Product of roots, $P = \frac{c}{a}$

Substitute the values of $a$, $b$, and $c$ into these formulas to find the sum and product of the roots.

So,

Sum of roots, $S = -\frac{2}{3}$

Product of roots, $P = \frac{0}{3} = 0$

Therefore, the sum of the roots is $-\frac{2}{3}$ and the product of the roots is $0$.