If the equation \(2x^2-3x+p=0\) has real roots, which condition on \(p\) is correct?

Correct answer: \(p\leq\frac{9}{8}\)

For a quadratic equation \(ax^2+bx+c=0\) to have real roots, its discriminant \(D=b^2-4ac\) must satisfy \(D\geq0\). Here, \(a=2\), \(b=-3\), and \(c=p\), so \(D=(-3)^2-4(2)(p)=9-8p\). Therefore, \(9-8p\geq0\), which gives \(p\leq\frac{9}{8}\). Option C is only one particular allowed value, while option D is not necessary. Exam tip: For real roots, first apply the condition \(D\geq0\).