If α and β are the zeroes of polynomial p(x)=3x²-4x-7 then form a quadratic polynomial whose zeroes are1/α and1/β
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The polynomial is 7x^2+4x-3
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Hey !
p(x) = 3x² - 4x - 7
α and β are the zeroes of p(x)
α + β = -b/a = 4/3
αβ = c/a = -7/3
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1/α and1/β are zeros of a polynomial
sum of zeros = 1/α + 1/β = α + β /αβ
= (4/3)/(-7/3)
= 4/3 x -3/7
= -4/7
product of zeros = (1/α) (1/β)
= 1/ αβ
= 1/-7/3
= -3/7
a quadratic polynomial :-
k{x² - (sum of zeros ) + (product of zeros)}
k{x² - 4/7x - 3/7}
k = 7 ,
7{x² - 4/7x - 3/7}
7x² -4x - 3
p(x) = 3x² - 4x - 7
α and β are the zeroes of p(x)
α + β = -b/a = 4/3
αβ = c/a = -7/3
=======================
1/α and1/β are zeros of a polynomial
sum of zeros = 1/α + 1/β = α + β /αβ
= (4/3)/(-7/3)
= 4/3 x -3/7
= -4/7
product of zeros = (1/α) (1/β)
= 1/ αβ
= 1/-7/3
= -3/7
a quadratic polynomial :-
k{x² - (sum of zeros ) + (product of zeros)}
k{x² - 4/7x - 3/7}
k = 7 ,
7{x² - 4/7x - 3/7}
7x² -4x - 3
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