Question

find the solution set.
3x² + 5x + 2 = 0
separate the two values with a comma.
enter the correct answer.

Explanation:

Step1: Use quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=3$, $b=5$, $c=2$.

Step2: Calculate discriminant

$\Delta = 5^2 - 4\times3\times2 = 25-24=1$

Step3: Compute first root

$x_1=\frac{-5+\sqrt{1}}{2\times3}=\frac{-5+1}{6}=\frac{-4}{6}=-\frac{2}{3}$

Step4: Compute second root

$x_2=\frac{-5-\sqrt{1}}{2\times3}=\frac{-5-1}{6}=\frac{-6}{6}=-1$

Answer:

$-1, -\frac{2}{3}$