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The roots of the quadratic equation $z^2 + az + b = 0$ are $2 - 3i$ and $2 + 3i$. What is $a+b$? Could you also explain how this is done? I'm kind of confused. 

 Jan 20, 2020
edited by Guest  Jan 20, 2020
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One of doing this is to work backwards.

   if the roots of an equation are p and q, then the equation is (z - p)(z - q)  =  0.

 

So, if the roots are  2 - 3i  and  2 + 3i,  then the equation is  [z - (2 - 3i)]·[z - (2 + 3i)]  =  0

If you multiply out the left-hand side of that equation and combine like terms, you get  z2 + 13  =  0

 

Since there is no z-term, the value of a is 0.

The value of b is 13.

 Jan 20, 2020

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