SOLUTION: Find a Quadratic equation with roots of (4+i) and (4-i)?

Question 216530: Find a Quadratic equation with roots of (4+i) and (4-i)?
Found 2 solutions by stanbon, drj:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find a Quadratic equation with roots of (4+i) and (4-i)?
----------------
Rewrite:
y = (x-(x+i))(x-(x-i))
------------------
y = ((x-4)-i)((x-4)+i)
--
Notice this has the form (a-b)(a+b)
---
y = [(x-4)^2 - (i)^2]
---
y = [x^2-8x+16+1]
---
y = x^2-8x+17
=================
Cheers,
Stan H.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Find a Quadratic equation with roots of (4+i) and (4-i)?

Step 1. We note that and

Step 2. To get a quadratic equation we use the given roots and then multiply

Step 3. Multiply and simplify

Step 4. We recognize the difference of squares given as .

Step 5. Then let A=x-4 and B=i

We can verify the above quadratic equation by using the quadratic formula given as

where a=1, b=-8, and c=17

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 -4 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 -4 is + or - .

The solution is

Here's your graph:

Ignoring the above graph, we have the same complex roots as given.

Step 6. ANSWER:

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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