Explanation

A quadratic has no real roots exactly when its discriminant is negative. For (d), Δ = 9² − 4·4·6 = 81 − 96 = −15 < 0, so 4x² + 9x + 6 = 0 has no real roots. The other three have positive discriminants (232, 108 and 60 respectively), hence real roots. The answer is option (d).