Find the x-intercepts.
-$$f ( x ) = 3 x ^ { 2 } - 5 x - 1$$
A) $\left( \frac { 5 + \sqrt { 37 } } { 6 } , 0 \right)$ and $\left( \frac { 5 - \sqrt { 37 } } { 6 } , 0 \right)$
B) $\left( \frac { - 5 + \sqrt { 37 } } { 6 } , 0 \right)$ and $\left( \frac { - 5 - \sqrt { 37 } } { 6 } , 0 \right)$
C) $\left( \frac { 5 + \sqrt { 13 } } { 6 } , 0 \right)$ and $\left( \frac { 5 - \sqrt { 13 } } { 6 } , 0 \right\}$
D) $\left\{ \frac { - 5 + \sqrt { 13 } } { 6 } , 0 \right)$ and $\left( \frac { - 5 - \sqrt { 13 } } { 6 } , 0 \right)$

Question

Quizplus · Accepted Answer

To find the x-intercepts of the quadratic equation $f(x) = 3x^2 - 5x - 1$, we set $f(x) = 0$ and solve for $x$ using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Here, $a = 3$, $b = -5$, and $c = -1$, leading to $x = \frac{5 \pm \sqrt{(-5)^2 - 4(3)(-1)}}{2(3)} = \frac{5 \pm \sqrt{25 + 12}}{6} = \frac{5 \pm \sqrt{37}}{6}$, which matches choice A.

Find the X-Intercepts f(x)=3x2−5x−1f ( x ) = 3 x ^ { 2 } - 5 x - 1f(x)=3x2−5x−1

Find the X-Intercepts $f ( x ) = 3 x ^ { 2 } - 5 x - 1$