Question

If α and β (α >β) are the zeroes of the polynomial −x² + 8x + 9, then (α − β) is equal to ______.

पर्याय

• −10

• 10

• ±10

• 8

Answer 1

If α and β (α >β) are the zeroes of the polynomial −x² + 8x + 9, then (α − β) is equal to ±10.

Explanation:

- x² + 8x + 9

α + β = `(-8)/-1 = 8`

α.β = `9/-1 = -9`

(α − β)² = (α + β)² - 4αβ

= 64 + 36 = 100

∴ α − β = `sqrt100`

α − β = ±10