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 Post subject: Finding quadratic equation (complex numbers)Posted: Tue, 19 Oct 2010 14:48:57 UTC
 Senior Member

Joined: Mon, 19 Apr 2010 13:45:05 UTC
Posts: 61
Find a quadratic equation with real coefficients that has 3 + i as one of its roots.

I am not sure what to

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 Post subject: Posted: Tue, 19 Oct 2010 15:25:27 UTC
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Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9633
If 3 + i is a root, then 3 - i has to be also.

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 Post subject: Re: Finding quadratic equation (complex numbers)Posted: Tue, 19 Oct 2010 15:57:33 UTC
 S.O.S. Oldtimer

Joined: Fri, 10 Oct 2008 15:35:23 UTC
Posts: 179
Location: Clarksville, ARkansas
TsAmE wrote:
Find a quadratic equation with real coefficients that has 3 + i as one of its roots.

I am not sure what to

Method 1:
Complex solutions to polynomial equations (with real coefficients) occur in complex conjugate pairs. Therefore, is also a root of this equation.
Multuply and set this equal to zero.

(Can you see that this will give you a difference of squares?)
.
Method 2:
The solution to the quadratic equation, is .
You know that one of the roots of the quadratic is , so .
The imaginary part of the root must come from taking the square root of a negative number. The real part is , so: .

Now that you know b, set .

Square both sides & solve for c.

Hopefully, you can take it from there to get your answer.

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