Represent the following situations in the form of quadratic equations

Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan's present age.

#### Solution

Let take Rohan's age = x years

Hence, his mother's age = x + 26

3 years from now

Rohan's age = x + 3

Age of Rohan's mother will = x + 26 + 3 = x + 29

The product of their ages 3 years from now will be 360 so that

(x + 3)(x + 29) = 360

⇒ x^{2} + 29x + 3x + 87 = 360

⇒ x^{2} + 32x + 87 = 360

⇒ x^{2} + 32x = 273

⇒ x^{2} + 32x - 273 = 0

⇒ x^{2} + 39x - 7x - 273 = 0

⇒ x2 + 39x - 7x - 273 = 0

⇒ x(x + 39) - 7(x + 39) = 0

⇒ (x + 39)(x - 7) = 0

⇒ x + 39 = 0 And x - 7 = 0

⇒ x = -39 And x = 7

Since,

Current age of Rohan = 7 year

Age of Rohan's mother = x + 26

= 7 + 26

= 33 year