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Find a quadratic polynomial whose zero …

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

Sia ? 6 years, 7 months ago

Let α=4 - {tex}\sqrt 5{/tex}
and β = 4 + {tex}\sqrt 5{/tex}
Sum of zeroes,
α+β = 4 - {tex}\sqrt 5{/tex} + 4 + {tex}\sqrt 5{/tex} = 8
αβ = (4 - {tex}\sqrt 5{/tex})(4 + {tex}\sqrt 5{/tex}) = 16 - 5 = 11
Quadratic polynomial
p(x) = x2 - (α+β)x +αβ
= x2 - 8x + 11

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