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)

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) (Show Source): You can put this solution on YOUR website!
Use the meaning of the discriminant.

has a discriminant, .

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