SOLUTION: If 4 + I and 4 - I are roots of the equation z^2 + az + b = 0 find the value of a and the value of b?

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Question 1017147: If 4 + I and 4 - I are roots of the equation z^2 + az + b = 0 find the value of a and the value of b?
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
If 4 + I and 4 - I are roots of the equation z^2 + az + b = 0 find the value of a and the value of b?
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(z - (4+i))*(z - (4-i)) = 0
z^2 - 8z + 17 = 0
a = -8, b = 17
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -4 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -4 is + or - .

The solution is , or
Here's your graph:
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