If the discriminant of a quadratic equation with real coefficients is \(D=2r^2+3\), where \(r\) is a real number, what is the correct conclusion about its roots?

Correct answer: The roots will always be real and distinct

Since \(r\) is real, \(r^2\ge 0\). Therefore, \(D=2r^2+3\ge 3>0\). For a quadratic equation, \(D>0\) indicates two real and distinct roots. Equal roots require \(D=0\), so option B is incorrect. Exam tip: remember the three discriminant tests: \(D>0\) for real and distinct roots, \(D=0\) for equal roots, and \(D<0\) for non-real roots.