MAHARASHTRA Class 10: Introduction to Quadratic Equations Videos | Introduction to Quadratic Equations

A quadratic equation has at most 2 roots.

Let the two consecutive positive integers be x and x + 1.

x(x + 1) = 240

x² + x - 240 = 0

x² + 16x - 15x - 240 = 0

(x + 16)(x - 15) = 0

x = 15 or x = −16

As the integers are positive, therefore x = 15.

So, the consecutive positive integers will be 15 and 16.

The required quadratic equation is 

(x - 15)(x - 16) = 0

i.e. x² - 31x + 240 = 0

Let the breadth of the plot be x metres.

Length = (2x + 1) m Area of plot = 528 m² (2x + 1)x = 528 2x² + x − 528 = 0