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I am trying to answer the following question:

The roots of the quadratic equation $ax^2-16x+25$ are $2+mi$ and $2-mi$, where $m>0$. Compute the sum of $a+m$.

Should the zeros of the equation be $x-(2+mi)$ and $x-(2-mi)$ or $x-2+mi$ and $x-2-mi$, or maybe something else? I really have no idea.

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It looks like something went wrong... By factoring you get that $ax^2 - 16x = x(ax-16) = 0$, so we have $x = 0$ of $x = \frac{16}{a}$ are the roots. –  andybenji Dec 2 '12 at 22:37
    
@andybenji it looks like someone who edited the problem made a mistake. I fixed it. Can you take another look? –  PygameNerd Dec 2 '12 at 22:45
    
Yeah definitely. –  andybenji Dec 2 '12 at 22:46
    
@andybenji ...and perhaps answer the question as well??? –  PygameNerd Dec 2 '12 at 22:49
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2 Answers

up vote 1 down vote accepted

The roots are given by the quadratic formula: $$x = \frac{16\pm \sqrt{16^2 - 4*25*a}}{2a}$$

We know that the real part of the roots will be $2$, so $\frac{16}{2a} = 2$, and $a = 4$. So we can plug that back into the quadratic formula. $$x = \frac{16\pm \sqrt{16^2 - 4*25*4}}{2*4}$$ and solve for your roots.

That should be more than enough to get you started.

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Substitute the roots back into the original problem for x. One at a time. You will end with a system of equations with two unknowns. Then you can solve for a and m.

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