find the quadratic polynomial whose zeros are 2+âš3 and 2-âš3
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Hi Mate !!
Given Zeros are :- ( 2 + √3 ) & ( 2 - √3 )
• Sum of the Zeros :-
2 + √3 + 2 - √3
= 4
• Product of the Zeros :-
( 2 + √3 ) ( 2 - √ 3 )
[ Using identity :- ( a + b ) ( a - b ) = a² - b² ]
( 2 )² - ( √ 3 )²
= 4 - 3
= 1
• To form the quadratic equations we have formula as :-
x² - ( Sum of Zeros )x +(Product of Zeros )
Putting value in it !
x² - 4x + 1 is the required quadratic equation !!
Given Zeros are :- ( 2 + √3 ) & ( 2 - √3 )
• Sum of the Zeros :-
2 + √3 + 2 - √3
= 4
• Product of the Zeros :-
( 2 + √3 ) ( 2 - √ 3 )
[ Using identity :- ( a + b ) ( a - b ) = a² - b² ]
( 2 )² - ( √ 3 )²
= 4 - 3
= 1
• To form the quadratic equations we have formula as :-
x² - ( Sum of Zeros )x +(Product of Zeros )
Putting value in it !
x² - 4x + 1 is the required quadratic equation !!
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