asap 4u q help (1 Viewer)

[amdspotter]

using crt 3-i should be another root and using those roots and long div i got another root as x^2-2x+2. i feel i went wrong somewhere if any1 could help that would be appreciated

 

[XXXPUMPERXXX]

step 1: click this link https://wolfreealpha.github.io/input/?i=x^4+-+8x^3+++24x^2+-+32x+++20+=+0&lang=en
step 2 : write your equation and press enter
step 3 :Like this reply

 

[amdspotter]

step 1: click this link https://wolfreealpha.github.io/input/?i=x^4+-+8x^3+++24x^2+-+32x+++20+=+0&lang=en
step 2 : write your equation and press enter
step 3 :Like this reply

thx m8, found out that i was indeed correct just that i had to simplify it further to get the complex roots

 

[icycledough]

You're right in getting x^2 - 2x + 2. So finding the discriminant, which is -4, will tell you that the quadratic has 2 complex roots. Through working out, you can complete the square and write it as x^2 - 2x + 1 + 1, or (x - 1)^2 + 1 = 0. From there, you should be able to get the last 2 roots. Thus, the initial quartic will have 4 complex roots. To double-check, you can use an online graphing calculator and the graph should look like a quadratic but with a flatter turning point.

 

[amdspotter]

You're right in getting x^2 - 2x + 2. So finding the discriminant, which is -4, will tell you that the quadratic has 2 complex roots. Through working out, you can complete the square and write it as x^2 - 2x + 1 + 1, or (x - 1)^2 + 1 = 0. From there, you should be able to get the last 2 roots. Thus, the initial quartic will have 4 complex roots. To double-check, you can use an online graphing calculator and the graph should look like a quadratic but with a flatter turning point.

Thanks yep I followed those steps

 

[CLUELESS14]

View attachment 34251
using crt 3-i should be another root and using those roots and long div i got another root as x^2-2x+2. i feel i went wrong somewhere if any1 could help that would be appreciated

Use a combination of sum of roots and product of roots (because you already know two of them) and you should get it like any other year 11 polynomial question. I find it more convenient than long division where it's easier to make a mistake

 

[5uckerberg]

The second one is just sum of roots is 6 and product of roots is 10.

 

[icycledough]

Thanks yep I followed those steps

No worries