Question

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★ STANDARD QUESTION 55 ★

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Question is -

Form a quadratic equation whose roots are the numbers
$\frac{1}{10 - \sqrt{72} } \: \: and \: \: \frac{1}{10 + 6 \sqrt{2} }$



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Answer 1

Hey

The given roots are :-

1 / 10 - √ 72

and

1 / 10 + 6√2

So basically the form of quadratuc equation is :-

x² - ( sum of roots )x + product of roots .

For easy convenience ,

find out seperately :-

Sum of roots :-

( 1 / 10 + √72 ) + ( 1 / 10 - 6√2 )

=( 1 / 10 + √72 ) + ( 1 / 10 - √72 )

= ( 10 - √72 + 10 + √72 ) / ( 10 + √72 ) ( 10 - √72 )

= 20 / ( 10 ) ² - (√72 )²

= 20 / 100 - 72

= 20 / 28 –––( i )


Now , product of zeros :-

( 1 / 10 + √72 ) ( 1 / 10 - √72 )

= 1 / ( 10 + √72 ) ( 10 - √72 )

= 1 / ( 10 ) ² - (√72 ) ²

= 1 / 100 - 72

= 1 / 28 –––( ii ) .

Now , for quadratic equation ,

we will put the value from eq ( i ) & eq ( ii )

So ,

x² - ( sum of zeros )x + product of zeros

= x² - ( 20 / 28 ) x + 1 / 28

= x² - 20 x / 28 + 1 / 28

By taking LCM ,

=> 28x² - 20x + 1 / 28 = 0

=> 28x² - 30x + 1 = 0 .

So the required quadratic equation is :-

( 28x² - 30x + 1 ) .


thanks :)