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Answer 1

(11)

The given polynomial is

f(x) = 6x² + x - 2

Since α and β are the zeroes of f(x), by the relation between zeroes and coefficients, we get

• α + β = - 1/6
• αβ = - 2/6 = - 1/3

Now, α/β + β/α

= (α² + β²)/(αβ)

= {(α + β)² - 2αβ}/(αβ)

= {(- 1/6)² - 2 (- 1/3)}/(- 1/3)

= (1/36 + 2/3)/(- 1/3)

= (25/36)/(- 1/3)

= - 25/12

⇒ α/β + β/α = - 25/12

(12)

The given polynomial is

f(s) = 3s² - 6s + 4

Since α and β are zeroes of f(s), by the relation between zeroes and coefficients, we get

• α + β = - (- 6/3) = 2
• αβ = 4/3

Then, α/β + β/α + 2 (1/α + 1/β) + 3αβ

= (α² + β²)/(αβ) + 2 (β + α)/(αβ) + 3αβ

= {(α + β)² - 2αβ}/(αβ) + 2 (α + β)/(αβ) + 3αβ

= {2^2 - 2 (4/3)}/(4/3) + 2 (2)/(4/3) + 3 (4/3)

= (4 - 8/3)/(4/3) + 4/(4/3) + 3 (4/3)

= (4/3)/(4/3) + 4 (3/4) + 4

= 1 + 3 + 4

= 8

⇒ α/β + β/α + 2 (1/α + 1/β) + 3αβ = 8

Answer 2

Answer:

Q11 : -25/12  Q12: 8

Step-by-step explanation: