SOLUTION: Determine how many and the type of number (rational, irrational, imaginary, complex conjugates) that the solutions of the equation x^2-7x+17=0 will be. Justify.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Determine how many and the type of number (rational, irrational, imaginary, complex conjugates) that the solutions of the equation x^2-7x+17=0 will be. Justify.      Log On


   

Question 865093: Determine how many and the type of number (rational, irrational, imaginary, complex conjugates) that the solutions of the equation x^2-7x+17=0 will be. Justify.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-7x%2B17=0
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Degree two, so maybe two complex solutions.

Look at discriminant: %28-7%29%5E2-4%281%29%2817%29=49-68=highlight_green%28-19%3C0%29.
This means, two complex zeros containing imaginary components.

You can also go a little more and find those two solutions.
x=%287-sqrt%28-19%29%29%2F2=7%2F2-i%2Asqrt%2819%29%2F2
OR
x=7%2F2%2Bi%2Asqrt%2819%29%2F2