SOLUTION: find the equation whose roots are 5+3i

Question 224798: find the equation whose roots are 5+3i
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Find the equation whose roots are 5+3i.

Step 1. We note that and

Step 2. Roots are and since complex roots appear in pairs

Step 3. Then we have the following

For x=5+3i, subtract 5+3i from both sides of the equation.

Equation A

for x=5-3i, subtract 5-3ik from both sides of the equation

Equation B

Step 4. Multiply Equations A and B

Multiply out the terms using the FOIL method:

Step 4. ANSWER: The solution is

Let's check with the quadratic formula given as

where a=1, b=-10 and c=34.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -36 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -36 is + or - .

The solution is

Here's your graph:

Ignoring the graph below, we have complex roots to this quadratic to be the same ones as given in the problem.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

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