Mathematics: The roots of the quadratic equation $z^2 + az + b = 0$ are $2 - 3i$ and $2 + 3i$. what is $a+b$?

4 centimeters is 0.04 meters....

The roots of the quadratic equation $z^2 + az + b

Ответ:

rburd

15.03.2022

Mathematics

We know for our problem that the zeroes of our quadratic equation are (2-3i)

and

, which means that the solutions for our equation are x=2-3i

and

. We are going to use those solutions to express our quadratic equation in the form $a x^{2} +bx+c$ ; to do that we will use the zero factor property in reverse:
x=2-3i

Now, we can multiply the left sides of our equations:
$(x-2+3i)(x-2-3i)= x^{2} -2x-3ix-2x+4+6i+3ix-6i-3^2i^2$
= $x^{2}-4x+4-9i^{2}$
= $x^{2} -4x+4+9$
= $x^{2} -4x+13$
Now that we have our quadratic in the form $a x^{2} +bx+c$ , we can infer that a=1

and

; therefore, we can conclude that a+b=1+(-4)=1-4=-3

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The roots of the quadratic equation $z^2 + az + b = 0$ are $2 - 3i$ and $2 + 3i$. what is $a+b$?

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