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

Mathematics

1 answer:

Oxana [17]2 years ago

8 0

Answer:

x^2+2x+2

Step-by-step 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:

$x=\dfrac{-2\pm\sqrt{4-8}}{2}=\dfrac{-2\pm 4i}{2}=-1\pm i$

Hope this helps!

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