a quadratic polynomial whose zeroes are root 2 and root 6/2 are {where, k is a non zero constant]
a - k(x^2-(2+root3)x + root6)
b - k(root2x^2+ (2+root3)x + root6)
c - k(root2x^2-(2+root3)x+root6)
d - k(x^2-(2+root3)x-root6)
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Answers
Answer:
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Given : a quadratic polynomial whose zeroes are √2 and √6/2 are \ k is a non zero constant
To Find : quadratic polynomial
a k(x²-(2+√3)x + √6)
b k(√2x²+ (2+√3)x + √6)
c k(√2x²-(2+√3)x+√6)
d k(x²-(2+√3)x-√6)
Solution:
a quadratic polynomial whose zeroes are α and β
can be written as
k ( x² - (sum of zeroes)x + product of zeroes) where k ≠ 0
k ( x² - (α + β )x + αβ)
Here zeroes are √2 and √6/2
sum of zeroes = √2 + √6/2 = (1/√2)( 2 + √3 )
Product of zeroes = √2 * √6/2 = √12 / 2 = √3
sum of zeroes = (1/√2)( 2 + √3 )
Product of zeroes = √3
polynomial
= k ( x² -(1/√2)( 2 + √3 ) x + √3)
Taking 1/√2 common
= (k / √2 )( √2x² - ( 2 + √3 ) x + √6)
= k ( √2x² - ( 2 + √3 ) x + √6) k and k/√2 are same as k is any non zero constant
k ( √2x² - ( 2 + √3 ) x + √6)
k(√2x²-(2+√3)x+√6) is correct option
Quadratic polynomial is k(√2x²-(2+√3)x+√6)
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