Quadratic Equations Examples and Solutions

Application of quadratic equation

Quadratic equations are useful in daily life for finding solutions of some practical problems. We are now going to learn the same.
Ex. (1) There is a rectangular onion storehouse in the farm of Mr. Ratnakarrao at Tivasa. The length of rectangular base is more than its breadth by 7 m and diagonal is more than length by 1 m. Find length and breadth of the storehouse.

Solution : Let breadth of the storehouse be x m.
∴length = (x + 7) m, diagonal = x + 7 + 1 = (x + 8) m
By Pythagorus theorem

`x^2+(x+7)^2=(x+8)^2`

`x^2+x^2+14x+49=x^2+16x+64`

`therefore x^2+14x-16x+49-64=0`

`therefore x^2-2x-15=0`

`therefore x^2-5x+3x-15=0`

`therefore x(x-5)+3(x-5)=0`

`therefore (x-5) (x+3)=0`

`therefore x-5=0 or x+3=0`

`therefore x=5 or x=-3`

But length is never negative ∴x≠-3

∴x = 5 and x + 7 = 5 + 7 = 12

Length of the base of storehouse is 12m and breadth is 5m.