Use the quadratic formula to solve the equation.
-$5 x ^ { 2 } + 7 x + 9 = 0$
A) $\left\{ \frac { - 7 - \sqrt { 131 } } { 10 } , \frac { - 7 + \sqrt { 131 } } { 10 } \right\}$
B) $\left\{ \frac { 7 - \mathrm { i } \sqrt { 131 } } { 10 } , \frac { 7 + \mathrm { i } \sqrt { 131 } } { 10 } \right\}$
C) $\left\{ \frac { - 7 - \mathrm { i } \sqrt { 131 } } { 10 } , \frac { - 7 + \mathrm { i } \sqrt { 131 } } { 10 } \right\}$
D) $\left\{ \frac { 7 - \sqrt { 131 } } { 10 } , \frac { 7 + \sqrt { 131 } } { 10 } \right\}$

Question

Quizplus · Accepted Answer

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. For the equation $5x^2 + 7x + 9 = 0$, $a = 5$, $b = 7$, and $c = 9$. Plugging these values into the formula, the discriminant ($b^2 - 4ac$) is negative ($49 - 180 = -131$), indicating that the solutions involve complex numbers. Thus, the correct answer involves $\mathrm{i}\sqrt{131}$ and matches option C.

Use the Quadratic Formula to Solve the Equation 5x2+7x+9=05 x ^ { 2 } + 7 x + 9 = 05x2+7x+9=0

Use the Quadratic Formula to Solve the Equation $5 x ^ { 2 } + 7 x + 9 = 0$