NCERT Class X Chapter 4: Quadratic Equation Exercise 4.1 Question 2 (iii)

NCERT Class X Chapter 4: Quadratic Equation Exercise 4.1 2 (iii)

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.

Given:

Rohan’s mother is 26 years older than him.

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

To Find:

Quadratic equation representing the situation to find Rohan’s present age.

Formula:

WKT, future age = present age + number of years.

Solution:

Let Rohan’s present age (in years) = x
According to the given condition,
Rohan’s mother’s present age = (x + 26) years.
Rohan’s age 3 years from now (in years) = x + 3

Rohan’s mother’s age 3 years from now = (x + 26 + 3) = x + 29
According to the given condition,

the product of their ages 3 years from now is 360.

⇒ (x + 3) × (x + 29) = 360
Expand the left side:

⇒ x(x + 29) + 3(x + 29) = 360

⇒ x2 + 29x + 3x + 87 = 360

⇒ x2 + 32x + 87 = 360
Rearrange the equation into the standard quadratic form ax2 + bx + c = 0:

⇒ x2 + 32x + 87 - 360 = 0

⇒ x2 + 32x - 273 = 0

Result:

The situation can be represented by the quadratic equation:
x2 + 32x - 273 = 0.
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