Find the x-intercepts (if any) for the graph of the quadratic function.
-$$7 x ^ { 2 } + 8 x + 2 = 0$$
Give your answers in exact form.
A) $\left( \frac { - 4 \pm \sqrt { 2 } } { 7 } , 0 \right)$
B) $\left( \frac { - 4 \pm \sqrt { 2 } } { 14 } , 0 \right)$
C) $\left( \frac { - 8 \pm \sqrt { 2 } } { 7 } , 0 \right)$
D) $\left( \frac { - 4 \pm \sqrt { 30 } } { 7 } , 0 \right)$

Question

Quizplus · Accepted Answer

To find the x-intercepts of the quadratic equation $7x^2 + 8x + 2 = 0$, we use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 7$, $b = 8$, and $c = 2$. Plugging these values in, we get $x = \frac{-8 \pm \sqrt{(8)^2 - 4(7)(2)}}{2(7)} = \frac{-8 \pm \sqrt{64 - 56}}{14} = \frac{-8 \pm \sqrt{8}}{14}$. Simplifying $\sqrt{8}$ to $2\sqrt{2}$ and further simplifying gives $x = \frac{-8 \pm 2\sqrt{2}}{14} = \frac{-4 \pm \sqrt{2}}{7}$, which matches choice A.

Find the X-Intercepts (If Any) for the Graph of the Quadratic