Represent the following situation in the form of quadratic equations:R

1.	Represent the following situation 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 = 0 ⇒ x² + 32x – 273 = 0 ⇒ x² + 39x – 7x – 273 = 0 ⇒ x (x + 39) – 7 (x + 39) = 0 ⇒ (x – 7) (x + 39) = 0 ⇒ x = 7 or x = -39 ‘x’ being age cannot be negative. ∴ x = Present age of Rohan = 7 years.

Represent the following situation 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 = 0

⇒ x² + 32x – 273 = 0

⇒ x² + 39x – 7x – 273 = 0

⇒ x (x + 39) – 7 (x + 39) = 0

⇒ (x – 7) (x + 39) = 0

⇒ x = 7 or x = -39 ‘x’ being age cannot be negative.

∴ x = Present age of Rohan = 7 years.