Question

find quadratic polynomial whose zeros are 3 +√5and 3-√5​

Answer 1

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✨ solution :

Let required polynomial be f(X)

then , x-(3+√5) and x-(3-√5) are factors of f(X) .

then ,

[x - (3 + √5)] [x - (3 - √5) is required polynomial

= [x - 3 - √5] [x - 3 + √5]

= x - 3x + √5x - 3x + 9 - 3 √5 - √5x +

3 √5 - 5

= x² - 6x + 4

or...

zeroes = 3+root5 and 3-root5

product of zeroes= (3+root5)(3-root5)

= 9-5

=4

sum of zeroes=3+root5 + 3-root5

=6

we know f(x) = k(x2^ - sum of zeroes (x) + product of zeroes

= k(x2^ -6x +4) is yr required answer ...

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Answer 2

Answer:

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