Question

The roots of an equation are x=-1 plus or minus I the equation is x^2+ ?

Answer 1

x^2+2x+2

Explanation:

If the roots of the equation are -1\pm i, then by the zero product rule:

`x=-1\pm i \\\\x+1\pm i=0 \\\\(x+1+i)(x+1-i)=0\\\\x^2+x-ix+x+1-i+ix+i+1=0 \\\\x^2+2x+2=0`

You can confirm this with the quadratic equation:

`x=(-2\pm√(4-8))/(2)=(-2\pm 4i)/(2)=-1\pm i`

Hope this helps!