Question

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Answer 1

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Answer 2

Given polynomial is x^2 - x - 4.

Here, a = 1, b = -1, c = -4.

Given that α and β are the zeroes of quadratic equation, then

(1) Sum of zeroes = -b/a

α + β = -(-1)/1

α + β = 1.

(2) Product of zeroes = c/a

αβ = -4/1

αβ = -4

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(i) α^2 + β^2

We know that (α + β)^2 = α^2 + β^2 + 2αβ

= > (1)^2 = α^2 + β^2 + 2(-4)

= > 1 = α^2 + β^2 - 8

= > α^2 + β^2 = 9.

(ii) α^3 + β^3

We know that α^3 + β^3 = (α + β)(α^2 + β^2 - αβ)

= > (1)(9 - (-4))

= > (1)(9 + 4)

= > 13.

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