Find the nature of the roots of the quadratic equations. if real roots exist, find them.

$2x^2-3x+5=0$

The sum of the ages of two friends is$20$ years. Four years ago, the product of their ages in the years was 48. Is the situation possible? If so determine their present ages.

In a class test, the sum of Moulika's marks in Mathematics and English is $30$. If she got $2$ marks more in Mathematics and $3$ marks less in English, the product of her marks would have been $210$. Find her marks in the two subjects.

Find two numbers whose sum is $27$ and product is $182$.

Find two consecutive positive integers, sum of whose squares is $613$.

Write three quadratic equations one having two distinct real solutions, one having no real solution and one having exactly one real solution.

Which of the following is not quadratic equation?