Question

Solve the equation x4-6x3+11x2-10x+2=0 give that 2+√3 is a root of the equation

Answer 1

the given root is (2+√3)

the another root is(2-√3)

sum of roots=2+√3+2-√3=4

product of roots=(2-√3) (2+√3) =2^2-√3^2=4-3=1

the equation is x^2-4x+1=0

this is required factor

now see the attachment

the given equation divide by the required factor is x^2-2x+2

now see another attachment

the roots are 2+√3, 2-√3, 1+i, 1-i