Solve Equations That Are Quadratic in Form
Solve the equation by making an appropriate substitution.
-$$x ^ { 4 } - 4 x ^ { 2 } + 3 = 0$$
A) $\{ - 1,1 , - \sqrt { 3 } , \sqrt { 3 } \}$
B) $\{ - 1,1 , - \mathrm { i } \sqrt { 3 } , \mathrm { i } \sqrt { 3 } \}$
C) $\{ 1,3 \}$
D) $\{ 1 , \sqrt { 3 } \}$

Question

Quizplus · Accepted Answer

We can make the substitution $y=x^2$, which gives us the equation $y^2-4y+3=0$. This is a quadratic equation that can be factored as $(y-1)(y-3)=0$. Substituting back $x^2$ for $y$, we get $x^4-4x^2+3=(x^2-1)(x^2-3)=0$. This gives us the solutions $x=\pm1$ and $x=\pm\sqrt{3}$. Therefore, the answer is A.

Solve Equations That Are Quadratic in Form Solve the Equation x4−4x2+3=0x ^ { 4 } - 4 x ^ { 2 } + 3 = 0x4−4x2+3=0

Solve Equations That Are Quadratic in Form
Solve the Equation $x ^ { 4 } - 4 x ^ { 2 } + 3 = 0$