If \(a\) is a real number, what is the nature of the roots of the equation \(2x^2-4ax+(2a^2-3)=0\)?

Correct answer: Always real and distinct

For the quadratic equation, \(A=2\), \(B=-4a\), and \(C=2a^2-3\). Its discriminant is \(D=B^2-4AC=(-4a)^2-4(2)(2a^2-3)=16a^2-16a^2+24=24\). Since \(D=24>0\) for every real value of \(a\), the roots are always real and distinct. Hence option A is correct; equal roots would require \(D=0\). Exam tip: in parameter-based questions, simplify the discriminant fully and check whether its sign depends on the parameter.