If alpha and ? Are zeroes of p(x)=x2+ 3x+7,find polynomial whose zeroes are 1/alpha+ 1/?
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Let α and β are zeroes of polynomial x²+3x +7 =0
α+β = -3
αβ = 7
now, 1/(αβ) = 1/7
and (1/α + 1/β ) = (α+β)/αβ = -3/7
required polynomial will be
x² - (-3/7)x + (1/7) = 0
⇒7x² +3x +1 =0
as we know that if α and β are roots then the equation will be
x² - (α+β)x + αβ =0
α+β = -3
αβ = 7
now, 1/(αβ) = 1/7
and (1/α + 1/β ) = (α+β)/αβ = -3/7
required polynomial will be
x² - (-3/7)x + (1/7) = 0
⇒7x² +3x +1 =0
as we know that if α and β are roots then the equation will be
x² - (α+β)x + αβ =0
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