Find a quadratic polynomial one of whose zero is 3+root 2 and the sum of it zero is 6
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Sum of zeroes = 6
First zero = 3 + root2
Second zero = 6 - (3+ root2)
= 6 - 3 - root2
= 3 - root2
Product of zeroes = (3+ root2) (3-root2)
= (3)^2 - (root2) ^2
= 9 - 2
= 7
Required polynomial = x^2 - (sum of zeroes)x + (Product of zeroes)
= x^2 -6x +7
First zero = 3 + root2
Second zero = 6 - (3+ root2)
= 6 - 3 - root2
= 3 - root2
Product of zeroes = (3+ root2) (3-root2)
= (3)^2 - (root2) ^2
= 9 - 2
= 7
Required polynomial = x^2 - (sum of zeroes)x + (Product of zeroes)
= x^2 -6x +7
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i hope i am right ok
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