Question

If alpha and beta are the zeroes of the polynomial p(x) =3x²-5x+6 then,find alpha/beta+beta/alpha

Answer 1

Answer:

3x 5x+6

15

15+6=21

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given -

• α and β are zeroes of polynomial p(x) = 3x² - 5x + 6

To Find -

• Value of α/β + β/α

→ α² + β²/αβ

Now,

As we know that :-

• αβ = c/a

→ αβ = 6/3

→ αβ = 2

• α + β = -b/a

→ α + β = -(-5)/3

→ α + β = 5/3

Squaring both sides :-

→ (α + β)² = (5/3)²

→ α² + β² = 25/9 - 2αβ

→ α² + β² = 25/9 - 2(2)

→ α² + β² = 25/9 - 4

→ α² + β² = 25-36/9

→ α² + β² = -11/9

Now,

The value of α² + β²/αβ is

→ -11/9×2

→ -11/18

Hence,

The value of α/β + β/α is -11/18.