Question

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.


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Answer 1

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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 = 0

⇒ x^2 + 32x – 273 = 0

Therefore, the age of Rohan and his mother,

satisfies the quadratic equation,

x^2 + 32x – 273 = 0,

which is the required representation of the problem mathematically.

Answer 2

Answer:

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Let the present age of rohan be x

then,her mother's age will be x+26

according to questtion after 3 year

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

x^2+29x+3x+87 =360

x^2 +32x-273 = 0

solve it by quadratic formula i.e.

-b+,- √b^2-4ac

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2a