What is the nature of the roots of the equation \\(8x^2+2x-3=0\\)?

Correct answer: Two real, rational and distinct roots

Here, \\(a=8, b=2, c=-3\\). Therefore, the discriminant is \\(D=b^2-4ac=2^2-4(8)(-3)=100\\). Since \\(D>0\\), the roots are real and distinct; since \\(100\\) is a perfect square, they are also rational. In fact, the roots are \\(\frac{1}{2}\\) and \\(-\frac{3}{4}\\). Exam tip: If \\(D>0\\) and the discriminant is a perfect square, the roots are real, distinct, and rational.