What is the nature of the roots of the equation \(3x^2+5x-2=0\)?

Correct answer: Two real, rational and distinct roots (\(D=49\))

Here, \(a=3\), \(b=5\), and \(c=-2\). Therefore, the discriminant is \(D=b^2-4ac=5^2-4(3)(-2)=49\). Since \(D>0\) and 49 is a perfect square, the roots are real, rational, and distinct. In fact, the roots are \(\frac{1}{3}\) and \(-2\). Option B applies when \(D=0\), while option C applies when \(D<0\). Exam tip: If \(D>0\) and is a perfect square, the roots are real, rational, and distinct.