(Q8)Represent the following situations in the form of quadratic equations:

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.

Answer

Let the present age of Rohan be x years

Then age of Rohan's mother = x + 26

After 3 years:

Age of Rohan would be = x + 3

Rohan's mother's age would be = (x + 26) + 3 = x + 29

By problem (x + 3)(x + 29) = 360
x(x + 29) + 3(x + 29) = 360
x2 + 29x + 3x + 87 = 360
x2 + 32x + 87 - 360
x2 + 32x - 273 = 0
x2 + 39x -x - 273 = 0
x(x + 39) - (x + 39) = 0
(x - )(x + ) = 0
x = or x = - 'x' being age can not be negative.
∴x = Present age of Rohan = years.