Problem

Determine whether the complex number is a solution of the equation.
\[
5-i ; x^{2}-10 x+26=0
\]
Is $5-i$ a solution of the equation $x^{2}-10 x+26=0$ ?
Yes
No

Answer

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Answer

\(\boxed{\text{No, } 5-i \text{ is not a solution of the equation } x^{2}-10 x+26=0}\)

Steps

Step 1 :To determine if a complex number is a solution to the equation, we can substitute the complex number into the equation and see if the equation holds true. If it does, then the complex number is a solution to the equation. If it doesn't, then it is not a solution.

Step 2 :In this case, we need to substitute \(5-i\) into the equation \(x^{2}-10 x+26=0\) and see if the left side equals to the right side.

Step 3 :Substitute \(x = 5 - i\) into the equation, we get \((-24 + (5 - i)^{2} + 10*i\).

Step 4 :The result of substituting \(5-i\) into the equation is not zero, which means that \(5-i\) is not a solution to the equation \(x^{2}-10 x+26=0\).

Step 5 :\(\boxed{\text{No, } 5-i \text{ is not a solution of the equation } x^{2}-10 x+26=0}\)

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