What is the nature of the roots of the equation \(4x^2+7x-2=0\)?

Correct answer: Two real, rational and distinct roots (\(D=81\))

Here, \(a=4, b=7, c=-2\). Therefore, the discriminant is \(D=b^2-4ac=7^2-4(4)(-2)=81\). Since \(D\) is positive and a perfect square, the roots are real, rational, and distinct. In fact, the roots are \(\frac{1}{4}\) and \(-2\). Option B is incorrect because a positive discriminant gives irrational roots only when it is not a perfect square. Exam tip: If \(D>0\) and is a perfect square, the roots are real, rational, and distinct.