In a quadratic equation ax2+bx+c=0, The discriminant, D=b2−4ac if b2−4ac<0 then the equation does not have real roots. ‌ A. ‌2x2+16x+3=0 ‌b2−4ac=(16)2−4(2)(3) ‌‌=256−24=232>0 (gives real roots) ‌ B. ‌2x2+10x−1=0 ‌b2−4ac=(10)2−4(2)(−1) ‌‌=100+8=108>0 (gives real roots) C. x2−8x+1=0 b2−4ac=(−8)2−4(1)(1) =64−4=60>0 (gives real roots) D. 4x2+9x+6=0 b2−4ac=(9)2−4(4)(6) =81−96=−15<0 (gives imaginary roots or not real) Hence, option (d) has the quadratic equation with no real roots.