What is the nature of the roots of the equation \(2x^2-7x+3=0\)?

Correct answer: two real and distinct

Here, \(a=2\), \(b=-7\), and \(c=3\). The discriminant is \(D=b^2-4ac=(-7)^2-4(2)(3)=49-24=25\). Since \(D>0\), the equation has two real and distinct roots. Option D is incorrect because the sum of the roots is \(-b/a=7/2\), which is positive, so both roots cannot be negative. Exam tip: \(D>0\) indicates real and distinct roots, \(D=0\) indicates real and equal roots, and \(D<0\) indicates no real roots.