Question

Express L={-2,2}in set-builder form

Answer 1

$l = (x \: \: such \: that \: {x}^{2} = 4)$

Answer 2

L = { x : x is a root of the equation x² = 4 }

Given :

The set L = { - 2 , 2 }

To find :

Express the set in set builder form

Solution :

Step 1 of 2 :

Write down the given set

The given set is L = { - 2 , 2 }

Step 2 of 2 :

Express the set in set builder form

We first find the quadratic equation whose zeroes are - 2 & 2

Sum of the zeroes = - 2 + 2 = 0

Product of the zeroes = - 2 × 2 = - 4

So the quadratic equation is given by

$\sf{x}^{2} - (sum \:of \:the \: zeros)x + (product \:of \:the \: zeros) = 0$

$\displaystyle \sf\implies {x}^{2} - 0.x +( - 4)= 0$

$\displaystyle \sf\implies {x}^{2} - 4= 0$

$\displaystyle \sf\implies {x}^{2} = 4$

Hence the required set in set builder form

L = { x : x is a root of the equation x² = 4 }

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