Question

solve for f. 3f² - 47f - 16 = 0 write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas. f =

Explanation:

Step1: Identify coefficients

For the quadratic equation $3f^{2}-47f - 16=0$, we have $a = 3$, $b=-47$, $c=-16$.

Step2: Use quadratic formula

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

$$\begin{align*} f&=\frac{-(-47)\pm\sqrt{(-47)^{2}-4\times3\times(-16)}}{2\times3}\\ &=\frac{47\pm\sqrt{2209 + 192}}{6}\\ &=\frac{47\pm\sqrt{2401}}{6}\\ &=\frac{47\pm49}{6} \end{align*}$$

\]

Step3: Find two solutions

For the plus - sign: $f=\frac{47 + 49}{6}=\frac{96}{6}=16$.
For the minus - sign: $f=\frac{47-49}{6}=\frac{-2}{6}=-\frac{1}{3}$.

Answer:

$16,-\frac{1}{3}$