Question

if x=-3+2i prove that x^2+6x+13=0

Answer 1

See just take it simple
We all know that complex roots always comes in pair i.e, if one root is a+bi then the other roots will always be a-bi [you can prove it from sridharacharya's formula]. So now the question is as simple as that.!
We know one root is
•x=-3+2i
So the other root will be
•x=-3-2i
=> Alpha+Beta =-6
=> Alpha•Beta =13
Then quadratic equation will be
K[x²-(alpha+beta)x+(alpha•beta)]=0
K[x²+6x+13]=0
Here, k is any integer(constant) which will not effect the factors.
Hope it helps!