Question

{x|25x^2-30x+9=0,x€Q} write in roster form

Answer 1

SOLUTION

TO DETERMINE

The set in roster form

$\sf{ \{ \: x: 25 {x}^{2} - 30x + 9 = 0 \: ,\: x \in \mathbb{Q} \}}$

CONCEPT TO BE IMPLEMENTED

SET

A set is a well defined collection of distinct objects of our perception or of our thought, to be conceived as a whole

Commonly we shall use capital letters A, B, C.... to denote sets and small letters a, b, c.... to denote objects ( or elements) of a set

EVALUATION

Here the given set is

$\sf{ \{ \: x: 25 {x}^{2} - 30x + 9 = 0 \: ,\: x \in \mathbb{Q} \}}$

Now

$\sf{25 {x}^{2} - 30x + 9 = 0 \: \: \: gives }$

$\sf{ \implies \: {(5x - 3)}^{2}= 0 \: \: \ }$

$\displaystyle \: \sf{ \implies \: x = \frac{3}{5} \: \: \ }$

So the required Set in roster form is

$\displaystyle \: \sf{ \bigg \{ \: \frac{3}{5} \bigg \} \: \ }$

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