Find the nature of the roots of the quadratic equation 2x²+3x+5=0.

Correct answer: No real roots

For a quadratic equation ax²+bx+c=0, the discriminant D=b²−4ac determines the nature of its roots. Here a=2, b=3 and c=5, so D=3²−4(2)(5)=9−40=−31. Because D is negative, the equation has no real roots; its two roots are complex conjugates. Therefore option C is correct. Equal real roots would require D=0, while two distinct real roots would require D>0. Option D is also incorrect because a non-degenerate quadratic equation does not have exactly one real root under the usual discriminant classification; the negative discriminant gives no real root at all.