Use factoring and the root method to solve the polynomial equation.
-$$x ^ { 4 } - 6 x ^ { 2 } + 9 = 0$$
A) 3
B) $- 3,3$
C) $\sqrt { 3 }$
D) $- \sqrt { 3 } , \sqrt { 3 }$

Question

Quizplus · Accepted Answer

This polynomial equation can be factored as a perfect square trinomial: $(x^2 - 3)^2 = 0$. Setting each factor equal to zero gives $x^2 - 3 = 0$, which solves to $x^2 = 3$. Taking the square root of both sides gives $x = \pm \sqrt{3}$, which corresponds to choice D.

Use Factoring and the Root Method to Solve the Polynomial x4−6x2+9=0x ^ { 4 } - 6 x ^ { 2 } + 9 = 0x4−6x2+9=0

Use Factoring and the Root Method to Solve the Polynomial $x ^ { 4 } - 6 x ^ { 2 } + 9 = 0$