Question

Hello, I need some help with question 7! Please show work as the instructions asked! If you want to see my answers to the other questions within the assignment, please let me know!

Answer 1

we have the polynomial

`4x^4+2x^2-12=0`

Change the variable

Let

U=2x^2

substitute

`\begin{gathered} (2x^2)^2+2x^2-12=0 \\ U^2+U-12=0 \end{gathered}`

Solve for U

using the formula

a=1

b=1

c=-12

substitute

`U=((-1)\pm√(1^2-4(1)(-12)))/(2(1))`
`\begin{gathered} U=(-1\pm7)/(2) \\ U=3 \\ U=-4 \end{gathered}`

Solve for x

For U=3

`\begin{gathered} 3=2x^2 \\ x^2=(3)/(2) \\ \\ x=\pm\sqrt{(3)/(2)}=\pm(√(6))/(2) \end{gathered}`

For U=-4

`\begin{gathered} -4=2x^2 \\ x^2=-2 \\ x=\pm i√(2) \end{gathered}`

Imaginary roots are

`\begin{gathered} x=i√(2) \\ x=-i√(2) \end{gathered}`

Real Roots are

`\begin{gathered} x=(√(6))/(2) \\ \\ x=-(√(6))/(2) \end{gathered}`

Code Piece is R