SOLUTION: determine nature of solutions of the equation. x^2+3x+5=0 a) two imaginary-number solutions b) one real-number rational solution c) two real-number irrational solutions d)

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Question 937927: determine nature of solutions of the equation.
x^2+3x+5=0
a) two imaginary-number solutions
b) one real-number rational solution
c) two real-number irrational solutions
d) two real-number rational solutions
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Use the meaning of the discriminant.

ax%5E2%2Bbx%2Bc=0 has a discriminant, b%5E2-4ac.

If discriminant is___________________Solutions are.
POSITIVE_____________________________Two Real
ZERO_________________________________One Real
NEGATIVE_____________________________Two Complex




Just form your equation's discriminant, compute it, and interpret its meaning.


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Your discriminant is -11, which is NEGATIVE, and the absolute value is not a square; which means the equation has two complex irrational solutions.