What is the correct formula of the discriminant in (ax^2+bx+c=0)?

Correct answer: D=b^2−4ac

For a quadratic equation written in standard form ax^2+bx+c=0, where a≠0, the discriminant is defined as D=b^2−4ac. It is the expression under the square root in the quadratic formula x=(−b±√(b^2−4ac))/(2a). The value of D determines the nature of the roots: D>0 gives two real distinct roots, D=0 gives two equal real roots, and D<0 gives non-real conjugate roots. Therefore option A is correct. Options B and C incorrectly interchange the roles of the coefficients, while option D omits the square on b. Correctly identifying a, b and c before substitution prevents these common errors.