Write the zeroes of the polynomial 2+root 3 and 2-root 3
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Solution :
Let m , n are two zeroes of the
polynomial ,
given m = 2+√3 , n = 2-√3
i ) sum of the zeroes
= m + n
= 2+√3 + 2 - √3
= 4
ii ) product of the zeroes
= mn
= ( 2+√3)(2-√3)
= 2² - ( √3 )²
= 4 - 3
= 1
Therefore ,
Required polynomial
= x² - ( m+n)x + mn
= x² - 4x + 1
•••••
Let m , n are two zeroes of the
polynomial ,
given m = 2+√3 , n = 2-√3
i ) sum of the zeroes
= m + n
= 2+√3 + 2 - √3
= 4
ii ) product of the zeroes
= mn
= ( 2+√3)(2-√3)
= 2² - ( √3 )²
= 4 - 3
= 1
Therefore ,
Required polynomial
= x² - ( m+n)x + mn
= x² - 4x + 1
•••••
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