If α and β are the zeros of the polynomial f(x) = x2 + x – 2, fi

1.	If α and β are the zeros of the polynomial f(x) = x2 + x – 2, find the value of (1/α – 1/β)
Answer» Given: α and β are zeroes of f(x) = x² + x – 2 To find: (1/α – 1/β) α + β = Sum of zeros = -(coefficient of x)/(coefficient of x²) = -1 α β = Product of zeros = (constant term)/(coefficient of x²) = -2 Now, (1/α – 1/β) = (β – α)²) / αβ = (β + α)² – 4αβ) / (αβ)² = 9/ 4

If α and β are the zeros of the polynomial f(x) = x2 + x – 2, find the value of (1/α – 1/β)

Answer»

Given: α and β are zeroes of f(x) = x² + x – 2

To find: (1/α – 1/β)

α + β = Sum of zeros = -(coefficient of x)/(coefficient of x²) = -1

α β = Product of zeros = (constant term)/(coefficient of x²) = -2

Now,

(1/α – 1/β) = (β – α)²) / αβ

= (β + α)² – 4αβ) / (αβ)²

= 9/ 4