Represent the following situation in the form of a quadratic equation:

The product of two consecutive positive integers is $306$. We need to find the integers.

Represent the following situation in the form of quadratic equation:

A train travels a distance of $480 \mathrm{k}\mathrm{m}$ at a uniform speed. If the speed had been $8 \mathrm{k}\mathrm{m}/\mathrm{h}$ less, then it would have taken $3$ hours more to cover the same distance. We need to find the speed of the train.

Find the roots of the following quadratic equations by factorization.

Find the roots of the following quadratic equations by factorization.

Find the roots of the given quadratic equation by factorisation:

$2x^2-x+\frac{1}{8}=0$

Find the roots of the given quadratic equations by factorisation:

Represent the following situation mathematically: John and Jivanti together have $45$ marbles. Both of them lost $5$ marbles each, and the product of the number of marbles they now have is $124$. We would like to find out how many marbles they had to start with.