The discriminant of the equation x^2+2x√3+3=0 is zero. Hence, its roots are:

1955 AMC 12 Problem 18

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18.

The discriminant of the equation

x^2+2x\sqrt3+3=0

is zero. Hence, its roots are:

real and equal

rational and equal

rational and unequal

irrational and unequal

imaginary

Use the quadratic formula with the discriminant term equal to zero

Then inspect the resulting value

-\frac{b}{2a}

for the requested classifications

The quadratic formula gives

x=\frac{-2\sqrt3}{2}=-\sqrt3

twice because the discriminant is zero. The root is irrational, but the requested description that applies is “real and equal.”

Thus, the correct answer is A.