Question

If α, β are the zeroes of the quadratic polynomial x

2

+3x+6, Find the value of

(α/β+β/α)​

Answer 1

Answer :

-½

Explanation :

Given polynomial,

⇒x² + 3x + 6

On comparing with ax² + bx + c we get,

• a = 1
• b = 3
• c = 6

Then,

• α + β = -b/a = -3
• αβ = c/a = 6

Finding (α/β + β/α)

⇒ α² + β²/αβ

⇒ (α + β)² - 2αβ/αβ

On substituting the values,

⇒ (-3)² - 2(6)/6

⇒ 9 - 12/6

⇒ -3/6

⇒ -½

Required answer : -½