The product of the digits of a two-digit number is $14$. The number obtained by interchanging the digits is $45$ more than the original number. Find the original number.

Find the roots of the following quadratic equation,if they exist,using the quadratic formula: $3x^{2} - 5x + 2 = 0$.

$A$ rectangular park is to be designed whose breadth is $3\, m$ less than its length. Its area is to be $4\, m^2$ more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude $12\, m$ (see Figure). Find its length and breadth.

Obtain the roots of the following equation using the method of 'completing the square': $3y^{2} + 7y - 20 = 0$.

Find two consecutive odd positive integers,the sum of whose squares is $290$.

The quadratic equation .............. has a root $x=3$.