Represent the following situations in the form of quadratic equation:

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

Check whether the following are quadratic equation:

(x - 3)(2x + 1) = x(x + 5)

Check whether the following are quadratic equation:

x² - 2x = ( - 2)(3 - x)

Check whether the following are quadratic equation:

(2x - 1) (x - 3) = (x + 5)(x - 1)

Represent the following situations in the form of quadratic equation:

The area of a rectangular plot is 528m². The length of the plot is one meter more than twice its breadth. We need to find the length and breadth of the plot.

Represent the following situations in the form of quadratic equation:

Rohan’s mother is 26 years older than him. The product of their ages after 3 years will be 360 years. We need to find Rohan’s present age.

Represent the following situations in the form of quadratic equation:

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

Check whether the following are quadratic equation:

x³ - 4x² - x + 1 = (x - 2)³

Check whether the following are quadratic equation:

(x + 1)² = 2(x - 3)

Check whether the following are quadratic equation:

(x - 2)(x + 1) = (x - 1) (x + 3)

Check whether the following are quadratic equation:

(x + 2)³ = 2x(x² - 1)