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Brainiest to whoever gets this right first! 20 points!

The roots of the quadratic equation $z^2 + az + b = 0$ are $-7 + 2i$ and $-7 - 2i$. What is $a+b$?

Respuesta :

LammettHash

You know the roots to the quadratic, so you know how the quadratic can be factorized:

[tex]z^2+az+b=(z-(-7+2i))(z-(-7-2i))=(z+7-2i)(z+7+2i)[/tex]

Expanding the right side gives

[tex]z^2+az+b=z^2+14z+4[/tex]

Matching up the coefficients tells us [tex]a=14[/tex] and [tex]b=4[/tex], so [tex]a+b=18[/tex].

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