find quadratic equation whose roots are 7+-2√5
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Answered by
33
Answer:
x² - 14x + 29
Step-by-step explanation:
One root is α = 7 + 2√5. The other root is β = 7 - 2√5.
So the quadratic is...
( x - α ) ( x - β )
= x² - (α+β)x + αβ
Working out the coefficients:
α+β = (7+2√5) + (7-2√5) = 7+7 = 14
αβ = (7+2√5)(7-2√5) = 7² - (2√5)² = 49 - 4×5 = 49 - 20 = 29
So the quadratic is
x² - 14x + 29
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Answer:
Step-by-step explanation:
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