Question

If α and β are the zeroes of the polynomial x² + 2x + 1, then `1/α + 1/β` is equal to ______.

Options

• –2

• 2

• 0

• 1

Answer 1

If α and β are the zeroes of the polynomial x² + 2x + 1, then `1/α + 1/β` is equal to –2.

Explanation:

Given, α and β are the zeroes of polynomial x² + 2x + 1.

∴ Sum of zeroes, (α + β) = `- 2/1` = –2

And product of zeroes, (αβ) = `1/1` = 1

Now, `1/α + 1/β = (α + β)/(αβ)`

= `- 2/1`

= –2