Reprsent the following situations in the form of quadratic equations :

1.	Reprsent 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.
Answer» Let the present age of Rohan be ‘x’, then His mother’s age will be (x + 26) After 3 years, Age of Rohan is (x + 3). After 3 years his mother’s age will be = (x + 26 + 3) = (x + 29) Then product of their ages is 360. ∴ (x + 3) (x + 29) = 360 x² + 29x + 3x + 87 = 360 x² + 32x + 87 = 360 x² + 32x + 87 – 360 = 0 x² + 32x – 273 = 0. This is required equation. Now, we have to solve for the value of ‘x’: x² + 32x – 273 = 0 x² + 39x – 7x – 273 = 0 x(x + 39) – 7(x + 39) = 0 (x + 39) (x – 6) = 0 If x + 39 = 0, then x = -39 If x – 6 = 0, then x = 7 Present age of Rohan’s mother = x + 26 = 7 + 26 = 33 years.

Reprsent 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.

Answer»

Let the present age of Rohan be ‘x’, then His mother’s age will be (x + 26)

After 3 years, Age of Rohan is (x + 3).

After 3 years his mother’s age will be

= (x + 26 + 3) = (x + 29)

Then product of their ages is 360.

∴ (x + 3) (x + 29) = 360

x² + 29x + 3x + 87 = 360

x² + 32x + 87 = 360

x² + 32x + 87 – 360 = 0

x² + 32x – 273 = 0.

This is required equation.

Now, we have to solve for the value of ‘x’:

x² + 32x – 273 = 0

x² + 39x – 7x – 273 = 0

x(x + 39) – 7(x + 39) = 0

(x + 39) (x – 6) = 0

If x + 39 = 0, then x = -39

If x – 6 = 0, then x = 7

Present age of Rohan’s mother

= x + 26

= 7 + 26 = 33 years.