Question

A quadratic polynomial whose zeroes are `2/5` and `(-1)/5` is ____________.

Options

• 25x² + 5x − 2

• 5x² − 2x + 1

• 5x² + 2x − 1

• 25x² − 5x − 2

Answer 1

A quadratic polynomial whose zeroes are `2/5` and `(-1)/5` is 25x² − 5x − 2.

Explanation:

Let α = `2/5` and β = `− 1/5` be the zeroes of the polynomial P(x).

Quadratic equation

x² − (α + β)x + αβ = 0

⇒ `x^2 − (2/5 + (−1/5)) x + 2/5 xx (− 1/5)` = 0

⇒ `x^2 − (2/5 − 1/5) x − 2/25` = 0

⇒ `x^2 − ((2 − 1)/5) x − 2/25` = 0

⇒ `x^2/1 − 1/5x − 2/25` = 0

⇒ `(25x^2 - 5x - 2)/25` = 0

⇒ 25x² − 5x − 2 = 0