Question

if alpha and beta are the zeros of the polynomials 5x²-5x+1 find alpha⁴ /beta⁴ + beta²/alpha​

Answer 1

Answer:

The given polynomial is

p (x) = 5x² + 5x + 1

Since α and β are the zeroes of p (x),

α + β = - 5/5

⇒ α + β = - 1 ...(1)

and

αβ = 1/5 ...(2)

(i) Now, α² + β²

= (α + β)² - 2αβ

= (- 1)² - 2 (1/5)

= 1 - 2/5

= (5 - 2)/5

= 3/5

(ii) Now, α^(- 1) + β^(- 1)

= 1/α + 1/β

= (β + α)/(αβ)

= (- 1)/(1/5)

= - 5

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