Discussion

Question:

If α and ß are the roots of the equation x² – 3x + 5 = 0, then what is the value of α³ + ß³?

Explanation:

We know, (α + ß)³ = α³ + ß³ + 3αß(α + ß)

⇒ α³ + ß³ = (α + ß)³ - 3αß(α + ß) …(1)

Here, α + ß = sum of the roots = - (-3/1) = 3

and, αß = product of the roots = 5/1 = 5.

Substituting these values in (1), we get

α³ + ß³ = (3)³ – 3 × 5 × (3)

⇒ α³ + ß³ = 27 – 45 = -18

Hence, option (b).

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