Question

If alpha and beta are the zeroes of the polynomial p (x) = 5x²+5x+1 find the value of 1/alpha ²+1/beta², 1/alpha +1/beta - 2 alpha beta, alpha ²+beta ².​

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

Answer 2

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