Padhona

Mathematics · Quadratic Equations · NCERT Examples

Example 1

A complete, independently verified solution for NCERT Example 1.

Mathematics · Chapter 4 · NCERT Examples

Download PDF
Verified NCERT questions and solutionsSolutions are checked independently and follow the supplied NCERT chapter edition.

NCERT Example

Example 1

forming quadratic equations · word problems

Represent the following situations mathematically.

  1. John and Jivanti together have 45 marbles. After each loses 5 marbles, the product of the numbers left is 124.

  2. A cottage industry makes x toys in a day. The cost per toy is ₹(55 − x), and the total cost is ₹750.

Solution

  1. Let John initially have x marbles; Jivanti has 45 − x. After the losses:

    (x−5)(40−x)=124(x-5)(40-x)=124
    −x2+45x−324=0⇒x2−45x+324=0-x^2+45x-324=0\Rightarrow x^2-45x+324=0

  2. Let x be the number of toys. Then:

    x(55−x)=750x(55-x)=750
    x2−55x+750=0x^2-55x+750=0

Final answer

The required equations are x² − 45x + 324 = 0 and x² − 55x + 750 = 0.