Question

If alpha and beta are zeroes of polynomial f(x)=x2-px+q then find values of alpha^2+beta^2

Answer 1

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Answer 2

Answer:

α^2 + β^2 = p^2 - 2q

Step-by-step explanation:

We have been given that α and β are the zeroes of polynomial x² + px + q.

Finding the relationship between Zeroes :

Sum of Zeros, (α + β) = -b/a

=> Sum of Zeros, (α + β) = -p/1

=> Sum of Zeros, (α + β) = -p

Product of Zeros , αβ = c/a

=> Product of Zeros, αβ = q/1

=> Product of Zeros, αβ = q

Now, We have to find the value of (α^2 + β^2) .

We know that,

a^2 + b^2 = (a + b)^2 - 2ab

Then,

α^2 + β^2 = (α + β)^2 - 2αβ

Now, by applying the given values, we get,

(α + β)^2 - 2αβ = (-p)^2 - 2q = p^2 - 2q

Hence,

α^2 + β^2 = p^2 - 2q