Find a quadratic polynomial whose zero are 4+√5 and 4-√5

1.	Find a quadratic polynomial whose zero are 4+√5 and 4-√5
Answer» Let α=4\xa0-\xa0{tex}\\sqrt 5{/tex}and\xa0β = 4 +\xa0{tex}\\sqrt 5{/tex}Sum of zeroes,α+β = 4\xa0-\xa0{tex}\\sqrt 5{/tex}\xa0+ 4\xa0+\xa0{tex}\\sqrt 5{/tex}\xa0= 8αβ = (4\xa0-\xa0{tex}\\sqrt 5{/tex})(4 +\xa0{tex}\\sqrt 5{/tex}) = 16 - 5 = 11Quadratic polynomialp(x) = x2\xa0- (α+β)x +αβ= x2\xa0-\xa08x + 11

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