select all of the following equation(s) that are quadratic in form.\n$x^{4}-6x^{2}-27 = 0$\n$3x^{4}=2x$\n$2(x…

select all of the following equation(s) that are quadratic in form.\n$x^{4}-6x^{2}-27 = 0$\n$3x^{4}=2x$\n$2(x + 5)^{4}+2x^{2}+5 = 0$\n$6(2x + 4)^{2}=(2x + 4)+2$\n$6x^{4}=-x^{2}+5$\n$8x^{4}+2x^{2}-4x = 0$\ndone

select all of the following equation(s) that are quadratic in form.\n$x^{4}-6x^{2}-27 = 0$\n$3x^{4}=2x$\n$2(x + 5)^{4}+2x^{2}+5 = 0$\n$6(2x + 4)^{2}=(2x + 4)+2$\n$6x^{4}=-x^{2}+5$\n$8x^{4}+2x^{2}-4x = 0$\ndone

Answer

Answer:

  1. $x^{4}-6x^{2}-27 = 0$
  2. $6(2x + 4)^{2}=(2x + 4)+2$
  3. $6x^{4}=-x^{2}+5$

Explanation:

Step1: Recall quadratic - form definition

A quadratic - form equation can be written as $au^{2}+bu + c = 0$, where $u$ is an algebraic expression.

Step2: Analyze $x^{4}-6x^{2}-27 = 0$

Let $u = x^{2}$, then the equation becomes $u^{2}-6u - 27=0$, which is quadratic in form.

Step3: Analyze $3x^{4}=2x$

Rewrite as $3x^{4}-2x = 0$. If we let $u = x^{2}$, we get $3u^{2}-2\sqrt{u}=0$, not quadratic in form.

Step4: Analyze $2(x + 5)^{4}+2x^{2}+5 = 0$

There is no simple substitution to get a quadratic - form equation.

Step5: Analyze $6(2x + 4)^{2}=(2x + 4)+2$

Let $u = 2x + 4$, then the equation becomes $6u^{2}-u - 2=0$, which is quadratic in form.

Step6: Analyze $6x^{4}=-x^{2}+5$

Let $u = x^{2}$, then the equation becomes $6u^{2}+u - 5=0$, which is quadratic in form.

Step7: Analyze $8x^{4}+2x^{2}-4x = 0$

If we let $u = x^{2}$, we get $8u^{2}+2u-4\sqrt{u}=0$, not quadratic in form.