Chapter A.6, Problem 70AYU

To determine

To solve: $3x^2+5x+2=0$

Answer to Problem 70AYU

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

Explanation of Solution

$3x^2+5x+2=0$

$a{x}^2 + bx + c = 0$ Compare to standard form.

With $a=3, b= 5$, and $c=2$, the discriminant is $b^2-4ac={\left(5\right)}^2-4\left(3\right)\left(2\right)=1$.

Since $b^2-4ac>0$, there are two real solutions. Use the quadratic formula with $a=3, b= 5, c=2$ and $b^2-4ac=1$.

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-5\pm \sqrt{1}}{2\left(3\right)}=\frac{-5\pm 1}{6}$

$x=\frac{-5+1}{6}=-\frac{4}{6}=-\frac{2}{3}$ and $x=\frac{-5-1}{6}=-1$

Therefore $x=-\frac{2}{3}, -1$.