Solve the quadratic equation using the method that seems most appropriate to you. $9 x ^ { 4 } + 11 x ^ { 2 } - 48 = 0$
A) $\left\{ \pm i \sqrt { 3 } , \pm \frac { 4 } { 3 } \right\}$
B) $\left\{ i \sqrt { 3 } , \frac { 4 } { 3 } \right\}$
C) $\left\{ \pm i \sqrt { 3 } , \frac { 4 } { 3 } \right\}$
D) $\left\{ i \sqrt { 3 } , \pm \frac { 4 } { 3 } \right\}$

Question

Quizplus · Accepted Answer

Let $y = x^2$, transforming the equation into a quadratic form: $9y^2 + 11y - 48 = 0$. Solving this quadratic equation yields $y = \frac{4}{3}$ and $y = -3$. Substituting back $x^2 = y$, we get $x^2 = \frac{4}{3}$ and $x^2 = -3$, leading to the solutions $\left\{ \pm \frac{4}{3}, \pm i\sqrt{3} \right\}$.

Solve the Quadratic Equation Using the Method That Seems Most 9x4+11x2−48=09 x ^ { 4 } + 11 x ^ { 2 } - 48 = 09x4+11x2−48=0

Solve the Quadratic Equation Using the Method That Seems Most $9 x ^ { 4 } + 11 x ^ { 2 } - 48 = 0$