Question

If alpha and beta are the series of the quadratic polynomial 2x^2 - 5x + 3 then find the value of alpha/beta + beta/alpha

Answer 1

Step-by-step explanation:

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Answer 2

Given:

α and β are the zeroes of the polynomial 2x² - 5x + 3 .

• a = 2

• b = -5

• c = 3

To find out:

Find the value of α/β + β/α ?

Solution:

★Sum of zeroes:

α + β = -b/a

⇒ - ( - 5 ) / 2

⇒ 5/2

★Product of zeroes:

αβ = c/a

⇒ 3/2

Now,

α/β + β/α [ Given ]

⇒ α² + β² /αβ

We know that,

α² + β² = ( α + β )² - 2αβ

⇒ ( α + β )² - 2αβ / αβ

☆Putting the values, we get

⇒ ( 5/2 )² - 2 × 3/2 / 3/2

⇒ 25/4 - 3 / 3/2

⇒ 25 - 12/4 / 3/2

⇒ 13/4 × 2/3

⇒13/6

Thus ,the value of α/β + β/α is 13/6 .