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4.
The given polynomial is
p(y) = 5y² - 7y + 1
Since α and β are the zeroes of p(y),
- α + β = - (- 7)/5 = 7/5
- αβ = 1/5
Then, 1/α + 1/β
= (β + α)/(αβ)
= (7/5)/(1/5)
= (7/5) × 5
= 7
5.
The given polynomial is
f(x) = x² - x - 4
Since α and β are the zeroes of f(x),
- α + β = - (- 1)/1 = 1
- αβ = (- 4)/1 = - 4
Then, 1/α + 1/β - αβ
= (β + α)/(αβ) - αβ
= 1/(- 4) - (- 4)
= - 1/4 + 4
= (- 1 + 16)/4
= 15/4
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