find the quadratic equation if the roots are (2-√3) and (2+√3)
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x = ( 2 - √3 ) , ( 2 + √3 )
[ x - ( 2 - √3 ) ] × [ x - ( 2 + √3 ) ]
= [ x - 2 + √3 ] × [ x - 2 - √3 ]
= [ ( x - 2 ) + √3 ] × [ ( x - 2 ) - √3 ]
= ( x - 2 )² - (√3)²
= x² - 4x + 4 - 3
= [ x² - 4x + 1 ].....
Hope it helps
x = ( 2 - √3 ) , ( 2 + √3 )
[ x - ( 2 - √3 ) ] × [ x - ( 2 + √3 ) ]
= [ x - 2 + √3 ] × [ x - 2 - √3 ]
= [ ( x - 2 ) + √3 ] × [ ( x - 2 ) - √3 ]
= ( x - 2 )² - (√3)²
= x² - 4x + 4 - 3
= [ x² - 4x + 1 ].....
Hope it helps
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