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# . 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.

Harshit Singh
one year ago
Dear student

Let us consider,
Age of Rohan’s = x years
Therefore, as per the given question,
Rohan’s mother’s age = x + 26
After 3 years, Age of Rohan’s = x + 3
Age of Rohan’s mother will be = x + 26 + 3
= x + 29
The product of their ages after 3 years will be equal to 360,
such that (x + 3)(x + 29) = 360
⇒ x^2 + 29x + 3x + 87 = 360
x^2 +32x+87=360

Thanks
KRIPA SHANKAR DWIVEDI
18 Points
9 months ago
Let rohans age=X
Rohans mother age=X+26
after 3 years
Rohan age=X+3
Rohan’s mother age=(X+26)+3=X+29
NOW A.T.Q
Product of age after 3 years=360
(X+3)(X+29)=360
X(X+29)+3(X+29)=360
X^2+29X+3X+87=360
X^2+32X+87−360=0
X^2+32X-272=0
It’s the form of
ax^2+bx+c=0
where a=1 b=32 c=−273
Ram Kushwah
110 Points
9 months ago
Let the age of Rohan=x years
AS mother is 26 older than Rohan
so Mother’s age=x+26
Now the product of their ages after 3 year will be 360
so (x+3)(x+3+26)=360
(x+3)(x+29)=360
x²+29x +3x +87=360
x²+32x-360+87=0

x²+32x-273=0
This is the quadratic equation formed

To find Rohan’s age:

x²+32x-273=0
x²+39x-7x-273=0
x(x+39)-7(x+39)=0
(x+39)(x-7)=0
x= -39 or 7

Age can not be negative
So Rohan’s age= 7 years