What is the nature of roots of the equation (7x^2-10x+3=0)?

Correct answer: Real and distinct

The standard test for the nature of roots is the discriminant D=b^2−4ac. Comparing 7x^2−10x+3=0 with ax^2+bx+c=0 gives a=7, b=−10 and c=3. Hence D=(−10)^2−4(7)(3)=100−84=16. Because D>0, the equation has two real and distinct roots, so option A is correct. We can also verify this by factorisation: 7x^2−10x+3=(7x−3)(x−1), giving roots 3/7 and 1, which are real and unequal. Equal real roots would require D=0, and non-real roots would require D<0. The roots are also not both negative, so option D is contradicted by their actual positive values.