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Answer 1

6.

The given polynomial is

f(x) = x² + x - 2

Since α and β are the zeroes of f(x),

• α + β = - 1/1 = - 1
• αβ = (- 2)/1 = - 2

Then, β - α

= √{(β + α)² - 4αβ}

= √{(- 1)² - 4 (- 2)}

= √{1 + 8}

= √9 = 3

∴ 1/α - 1/β

= (β - α)/(αβ)

= (3)/(- 2)

= - 3/2

7.

The given polynomial is

f(x) = 4x² - 8kx - 9

Let, the two zeroes are α and (- α)

Then, α + (- α) = - (- 8k)/4 = 2k

⇒ 2k = 0

⇒ k = 0