Solve.
-$5 x ^ { 4 } - 403 x ^ { 2 } - 162 = 0$
A) $- 9,9 , - \frac { \mathrm { i } \sqrt { 10 } } { 5 } , \frac { \mathrm { i } \sqrt { 10 } } { 5 }$
B) $9 , \frac { \mathrm { i } \sqrt { 10 } } { 5 }$
C) $- 9 i , 9 i , - \frac { i \sqrt { 10 } } { 5 } , \frac { i \sqrt { 10 } } { 5 }$
D) $- \frac { \sqrt { 10 } } { 5 } , \frac { \sqrt { 10 } } { 5 } , - 9,9$

Question

Quizplus · Accepted Answer

This equation is a quartic equation in the form of $ax^4 + bx^2 + c = 0$. By substituting $y = x^2$, it becomes a quadratic equation in $y$, which can be solved to find the roots in $x$. The correct roots are $-9, 9, -\frac{i\sqrt{10}}{5}, \frac{i\sqrt{10}}{5}$, indicating two real roots and two complex roots.

Solve - 5x4−403x2−162=05 x ^ { 4 } - 403 x ^ { 2 } - 162 = 05x4−403x2−162=0

Solve
- $5 x ^ { 4 } - 403 x ^ { 2 } - 162 = 0$