Question

1. solve for ( j). (3j^{2}-45j + 15=0) 2) write each solution as an integer, proper - fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas. (j=)

Explanation:

Step1: Identify coefficients

For the quadratic equation $3j^{2}-45j + 15=0$, we have $a = 3$, $b=-45$, $c = 15$.

Step2: Use quadratic formula

The quadratic formula is $j=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute the values:
\[

$$\begin{align*} j&=\frac{-(-45)\pm\sqrt{(-45)^{2}-4\times3\times15}}{2\times3}\\ &=\frac{45\pm\sqrt{2025 - 180}}{6}\\ &=\frac{45\pm\sqrt{1845}}{6}\\ &=\frac{45\pm3\sqrt{205}}{6}\\ &=\frac{15\pm\sqrt{205}}{2} \end{align*}$$

\]

Answer:

$j=\frac{15+\sqrt{205}}{2},\frac{15 - \sqrt{205}}{2}$