x^2 + 2x + 3 = 0 has

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two real rational roots

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two real irrational roots

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two equal real roots

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two equal rational roots

✓
two complex conjugate roots
x^2 + 2x + 3 = 0 has
two real rational roots
two real irrational roots
two equal real roots
two equal rational roots
two complex conjugate roots
Since the discriminant of the quadratic equation
b^24ac = 2^24\cdotp 1\cdotp 3 =8<0,
the roots of the quadratic equation will be two complex conjugate roots