Question

If alpha and beta r d zeros of px 3x2-6x+4. Find d value of alpha/beta+beta/alpha+2(1/alpha+1/beta)+3×alpha×beta.

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Answer 1

Answer :

  α/β + β/α + 2 (1/α + 1/β) + 3αβ = 8

Solution :

The given polynomial is

    P(x) = 3x² - 6x + 4

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

    α + β = - (- 6/3) = 2 .....(i)

    αβ = 4/3 .....(ii)

α/β + β/α

= (α² + β²)/(αβ)

= {(α + β)² - 2αβ}/(αβ)

= {2² - 2 (4/3)}/(4/3)

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

= {(12 - 8)/3}(4/3)

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

= 1

1/α + 1/β

= (β + α)/(αβ)

= 2/(4/3)

= 6/4

= 3/2

Now, α/β + β/α + 2 (1/α + 1/β) + 3αβ

= 1 + 2 (3/2) + 3 (4/3)

= 1 + 3 + 4

= 8