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Complex numbers question ;)

  • Thread starter Maatttt0
  • Start date
  • #1
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Homework Statement



One root of the equation x^2 + ax + b = 0 is 4 + 5i.

Write down the second root.

Homework Equations



N/a?

The Attempt at a Solution



My problem is it's a "write down" question which suggests no working required. This is probably so simple but I just don't know... I cannot do this even thought I know the later parts of the question. Thank you in advance ;)
 

Answers and Replies

  • #2
Pengwuino
Gold Member
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Write down the quadratic equation as you know it. The quadratic formula gives you two equations using one formula. What changes about the formula that gives you 2 separate solutions?
 
  • #3
37
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The plus or minus, so would it be 4 - 5i?
 
  • #4
Pengwuino
Gold Member
4,989
15
Yup! The quadratic formula gives solutions as

[tex]\[
\frac{{ - b}}{{2a}} \pm \frac{{\sqrt {b^2 - 4ac} }}{{2a}}
\]
[/tex]

However, you can rewrite the quadratic formula by pulling out a -1 from the term in the square root to get

[tex]\[
\frac{{ - b}}{{2a}} \pm i\frac{{\sqrt {4ac - b^2 } }}{{2a}}
[/tex]

So you can identify the 4 and the 5 with the real and imaginary parts of the equation.
 
  • #5
37
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Hehe, thank you so much :)

I know it was rather simple but my mind just wouldn't trigger.

Ty again ;)
 
  • #6
jbunniii
Science Advisor
Homework Helper
Insights Author
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179
By the way, that answer is correct only if [itex]a[/itex] and [itex]b[/itex] are both real. If the problem doesn't specify that they are, then the other root could be any complex number.
 

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