The answer is 26/7 it may seem to small to be the answer but just simplified it
The answer is not it is not because if you use the vertical line test it does not pass and if you plotted the coordinates then x would repeat multiple times
Hope this helps
Have a great day/night
Take some you time to focus on yourself, do calming activities wether it’s a walk, puzzle, or anything along those lines
now, this polynomial has roots of 3-i and 4i, namely 3 - i and 0 + 4i.
let's bear in mind that a complex root never comes all by her lonesome, her sibling is always with her, the conjugate, so if 3 - i is there, 3 + i is also coming along, likewise if 0 + 4i is there, her sibling 0 - 4i is also there.
![\bf \begin{cases} x=3-i\implies &x-3+i=0\\ x=3+i\implies &x-3-i=0\\ x=4i\implies &x-4i=0\\ x=-4i\implies &x+4i=0 \end{cases}\\\\[-0.35em] ~\dotfill\\\\ (x-3+i)(x-3-i)(x-4i)(x+4i)=\stackrel{y}{0} \\[2em] \underset{\textit{difference of squares}}{[(x-3)+i][(x-3)-i]}\underset{\textit{difference of squares}}{[x-4i][x+4i]}=0](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20x%3D3-i%5Cimplies%20%26x-3%2Bi%3D0%5C%5C%20x%3D3%2Bi%5Cimplies%20%26x-3-i%3D0%5C%5C%20x%3D4i%5Cimplies%20%26x-4i%3D0%5C%5C%20x%3D-4i%5Cimplies%20%26x%2B4i%3D0%20%5Cend%7Bcases%7D%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%28x-3%2Bi%29%28x-3-i%29%28x-4i%29%28x%2B4i%29%3D%5Cstackrel%7By%7D%7B0%7D%20%5C%5C%5B2em%5D%20%5Cunderset%7B%5Ctextit%7Bdifference%20of%20squares%7D%7D%7B%5B%28x-3%29%2Bi%5D%5B%28x-3%29-i%5D%7D%5Cunderset%7B%5Ctextit%7Bdifference%20of%20squares%7D%7D%7B%5Bx-4i%5D%5Bx%2B4i%5D%7D%3D0)
![\bf [(x-3)^2-i^2][x^2-(4i)^2]=y\implies [(x-3)^2-(-1)][x^2-(4^2i^2)]=0 \\[2em] [(x-3)^2-(-1)][x^2-(16(-1))]=0\implies [(x-3)^2+1][x^2+16]=0 \\[2em] [(x^2-6x+9)+1][x^2+16]=y\implies (x^2-6x+10)(x^2+16)=0 \\\\\\ x^4-6x^3+10x^2+16x^2-96x+160=0 \\\\\\ x^4-6x^3+26x^2-96x+160=0 \\\\\\ \stackrel{\textit{multiplying both sides by 4}}{4(x^4-6x^3+26x^2-96x+160)=4(0)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 4x^4-24x^3+104x^2-384x+640=y~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5B%28x-3%29%5E2-i%5E2%5D%5Bx%5E2-%284i%29%5E2%5D%3Dy%5Cimplies%20%5B%28x-3%29%5E2-%28-1%29%5D%5Bx%5E2-%284%5E2i%5E2%29%5D%3D0%20%5C%5C%5B2em%5D%20%5B%28x-3%29%5E2-%28-1%29%5D%5Bx%5E2-%2816%28-1%29%29%5D%3D0%5Cimplies%20%5B%28x-3%29%5E2%2B1%5D%5Bx%5E2%2B16%5D%3D0%20%5C%5C%5B2em%5D%20%5B%28x%5E2-6x%2B9%29%2B1%5D%5Bx%5E2%2B16%5D%3Dy%5Cimplies%20%28x%5E2-6x%2B10%29%28x%5E2%2B16%29%3D0%20%5C%5C%5C%5C%5C%5C%20x%5E4-6x%5E3%2B10x%5E2%2B16x%5E2-96x%2B160%3D0%20%5C%5C%5C%5C%5C%5C%20x%5E4-6x%5E3%2B26x%5E2-96x%2B160%3D0%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%204%7D%7D%7B4%28x%5E4-6x%5E3%2B26x%5E2-96x%2B160%29%3D4%280%29%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%204x%5E4-24x%5E3%2B104x%5E2-384x%2B640%3Dy~%5Chfill)