Question 2(iii)
Represent the following situations in the form of quadratic equations.
(iii) 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.
(iii) Let's 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.
(x+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+39)(x−7)=0
Either x+39=0orx−7=0
⇒x=−39 or x=7
As age cannot be in negative value,
x=7,Rohan's age = 7 years
Mother's age = 7+26=33 years