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The discriminant Δ = b² − 4ac sits under the square root in the quadratic formula, so its sign decides everything: positive gives two real roots, zero a repeated root, negative a complex conjugate pair.
Discriminant
Δ = b² − 4ac
Δ = 49 − 24 = 25, a perfect square, so the roots 3 and 0.5 are rational.
The roots are real but irrational, involving a surd such as √13.