If (D) is the discriminant of a quadratic equation and (D=0), what is the nature of roots?

Correct answer: Two equal real roots

The direct answer is B: the roots are two equal real roots. For a quadratic equation \(ax^2+bx+c=0\), the discriminant is \(D=b^2-4ac\), and the roots are \(\frac{-b\pm\sqrt D}{2a}\). If \(D=0\), then \(\sqrt D=0\), so both signs give the same value: \(\frac{-b}{2a}\). This value is real because the coefficients are real and \(a\ne0\). Therefore the equation has a repeated, or equal, real root. Option A is wrong because distinct roots require \(D>0\). Option B is correct. Option C is wrong because no real roots occur when \(D<0\). Option D is too specific and is not guaranteed: the repeated root may be positive, negative, or zero, depending on the coefficients. For example, \(x^2-4x+4=0\) has the equal real root 2. Exam cue: positive discriminant means two distinct real roots, zero means equal real roots, and negative means no real roots.