Find the x-intercepts (if any)for the graph of the quadratic function.
-$$3 x ^ { 2 } + 10 x + 6 = 0$$
Give your answers in exact form.
A) $\left( \frac { - 5 \pm \sqrt { 7 } } { 3 } , 0 \right)$
B) $\left( \frac { - 5 \pm \sqrt { 7 } } { 6 } , 0 \right)$
C) $\left( \frac { - 10 \pm \sqrt { 7 } } { 3 } , 0 \right)$
D) $\left( \frac { - 5 \pm \sqrt { 43 } } { 3 } , 0 \right)$

Question

Quizplus · Accepted Answer

The x-intercepts of a quadratic equation $ax^2 + bx + c = 0$ can be found using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. For the given equation $3x^2 + 10x + 6 = 0$, $a = 3$, $b = 10$, and $c = 6$. Plugging these values into the quadratic formula gives $x = \frac{-10 \pm \sqrt{10^2 - 4(3)(6)}}{2(3)} = \frac{-10 \pm \sqrt{100 - 72}}{6} = \frac{-10 \pm \sqrt{28}}{6}$. Simplifying $\sqrt{28}$ to $2\sqrt{7}$ and dividing both numerator terms by 2 gives $x = \frac{-5 \pm \sqrt{7}}{3}$, which corresponds to choice A.

Find the X-Intercepts (If Any)for the Graph of the Quadratic 3x2+10x+6=03 x ^ { 2 } + 10 x + 6 = 03x2+10x+6=0

Find the X-Intercepts (If Any)for the Graph of the Quadratic $3 x ^ { 2 } + 10 x + 6 = 0$