If the roots of the quadratic equation \(3x^2-4x+p=0\) are real, which condition on \(p\) is correct?

Correct answer: \(p\leq\frac{4}{3}\)

For a quadratic equation to have real roots, its discriminant must satisfy \(D\geq0\). Here, \(a=3\), \(b=-4\), and \(c=p\), so \(D=b^2-4ac=(-4)^2-4(3)(p)=16-12p\). Thus, \(16-12p\geq0\), which gives \(p\leq\frac{4}{3}\). Hence, option A is correct. Option B reverses the required inequality, while \(p<0\) is only a sufficient condition, not the complete condition. Exam tip: For questions about real roots, begin by applying \(D\geq0\).