The complex number 1 + ( 2)i is denoted by u. The polynomial x 4 + x 2 + 2x + 6 is denoted by p(x). (i) showing your working, verify that u is a root of the equation p(x) = 0, and write down a second complex root of the equation. [4] (ii) find the other two roots of the equation p(x) = 0
Answers
the complete question is
The complex number 1 (√2)i is denoted by u.
The polynomial x^4 x^2 2x 6 is denoted by p(x).
(i) Showing your working, verify that u is a root of the equation p(x) = 0, and write down a second
complex root of the equation.
(ii) Find the other two roots of the equation p(x) = 0
part i is simple but can anyone post the solution for part ii
its the question that came in nov 12 p31 gce A Level maths.
Thankx
Answer:
Step-by-step explanation:
p[x] = x4 +x2+ 2x +6
let x = 1+ root2i
x2 = [1+root2i][1+root2i] = 2root2i -1
x4 = [2root2i-1][2root2i -1] = -4root2i -7
p[x] = -4root2i -7 +2root 2i -1 +2[1+root2i]+6
p[x]=0
second part
roots = 1+-root2i
x=1+-root2i minus 1 on both sides x-1=+-root2i square on both sides obtaining x2-2x+3 perform long division x4+0x3+x2+2x+6/x2-2x+3
- x2+2x+2=0 is the result
- secondly perform quadratic formula obtaining -2+-2i/2