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Which quadratic equation has the roots -1+4i and -1-4i
A. X^2+2x+2=0
B. 2x^2+x+17=0
C. X^2+2x+17=0
D. 2x^2+x+2=0

Respuesta :

Answer:

C

Step-by-step explanation:

Solve the quadratic in answer choice C using the quadratic formula:

[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex].

Here a=1, b=2, and c=17.

Substitute and you'll have:

[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a} =\frac{-2+/-\sqrt{(-2)^2-4(1)(17)} }{2(1)}=\frac{-2+/-\sqrt{4-68}}{2)}[/tex]

[tex]\frac{-2+/-\sqrt{-64} }{2}=\frac{-2+/-8i }{2}=-1+/- 4i[/tex]