Question

if one zero of a quadratic polynomial is 2+√3, find the other zero.​

Answer 1

Answer:

Hi ,

Let p( x ) = x² - 4x + 1 ,

compare p( x ) with ax² + bx + c ,

a = 1 , b = -4 , c = 1

one zero = 2 + √3

Let second zero = p

sum of the zeroes = -b/a

p + ( 2 + √3 ) = - ( - 4 )

p = 4 - ( 2 + √3 )

p = 2 - √3

or

product of the zeroes = c/a

( 2 + √3 ) p = 1

p = 1/ ( 2 + √3 )

p = ( 2 - √3 ) / [ ( 2 + √3 ) ( 2 - √3 ) ]

= ( 2 - √3 ) / [ 2² - ( √3 )² ]

= ( 2 - √3 ) / ( 4 - 3 )

= 2 - √3

Therefore ,

required second zero of p( x )

p = 2 - √3

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