SOLUTION: 4 - i is a solution of a quadratic equation with real coefficients.Find the other solution.
How is this one done?
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Question 1207475: 4 - i is a solution of a quadratic equation with real coefficients.Find the other solution.
How is this one done?
Found 3 solutions by josgarithmetic, ikleyn, math_tutor2020:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
See the other partly solved example.
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.
The general theorem of algebra states that if a polynomial with real coefficients
has a complex number root a+bi, b=/= 0, then it has another complex number root a-bi, too.
According to this theorem, if 4-i is the root of your quadratic equation with real coefficients,
then it has the root 4+i, too. It is your other root.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
Answer: 4+i
Quick explanation: If a+bi is one root, then its paired counterpart (known as the complex conjugate) would be a-bi
This applies only when all of the coefficients are real numbers.
Another example: The root 2+i pairs up with 2-i
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Let's say you didn't know about the complex conjugate, or that you might be curious about an alternative pathway.
We can isolate the "i" term and square both sides to generate a quadratic from it.
Now let's apply the quadratic formula
or
or
We arrive at roots 4+i and 4-i to help confirm the answer.
This is a somewhat long-winded pathway to basically rephrase what I mentioned at the top.
If a+bi is one root, then a-bi is also included in the mix.
This only applies when all coefficients are real numbers.
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