Question

How many elements are there in the following sets :

(i) The set of all solutions of the quadratic equation x

2 = 25.

(ii) The set of squares of all natural numbers.

​

Answer 1

SOLUTION :-

TO DETERMINE :-

The number of elements in the following sets :

(i) The set of all solutions of the quadratic equation

$\sf{ {x}^{2} = 25 }$

(ii) The set of squares of all natural numbers.

CONCEPT TO BE IMPLEMENTED

SET : A set is a well defined collection of distinct objects

Finite Set : A set is said to be finite set if the set contains finite number of elements

Infinite Set : A set is said to be infinite set if the set contains infinite number of elements

EVALUATION :-

(i) Here the given Quadratic Equation is

$\sf{ {x}^{2} = 25}$

$\sf{ \implies x \: = \: \pm \: 5}$

Hence the set of all solutions of the quadratic equation is = { - 5, 5 }

Hence the number of elements in the set = 2

(ii) Here the set of natural numbers is

$\mathbb{N} = \{ 1,2,3,4,....... \}$

So the set of squares of all natural numbers

= { 1,4,9,16,.......}

So the set contains infinite number of elements

Hence the number of elements in the set is infinite

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