Find all valid real roots for the equation.
-$$x ^ { 6 } + 56 x ^ { 3 } - 512 = 0$$
A) $x = 2 , x = - 4$
B) $x = - 2 , x = 4$
C) $x = 2 , x = 4$
D) $x = - 2 , x = - 4$

Question

Quizplus · Accepted Answer

Let $y = x^3$, then the equation becomes $y^2 + 56y - 512 = 0$. Factoring or using the quadratic formula, we find $y = -64$ and $y = 8$. Thus, $x^3 = -64$ gives $x = -4$, and $x^3 = 8$ gives $x = 2$.

Find All Valid Real Roots for the Equation x6+56x3−512=0x ^ { 6 } + 56 x ^ { 3 } - 512 = 0x6+56x3−512=0

Find All Valid Real Roots for the Equation $x ^ { 6 } + 56 x ^ { 3 } - 512 = 0$