If \(v\) is any real number, which statement correctly describes the nature of the roots of \(2x^2-4vx+2v^2+5=0\)?

Correct answer: No real roots

Here, \(a=2\), \(b=-4v\), and \(c=2v^2+5\). Therefore, the discriminant is \(D=b^2-4ac=(-4v)^2-4(2)(2v^2+5)=16v^2-16v^2-40=-40\). Since \(D<0\) for every real value of \(v\), the equation has no real roots. Hence, option A is correct; option D is incorrect because the nature of the roots does not change with \(v\). Exam tip: a quadratic equation has no real roots when its discriminant is negative.