Symmetric functions of roots via sum and product (Vieta)

CAT has tested this idea 5 times across 5 papers, from 2017 to 2024. Solve one, and the others are the same method with different numbers or wording, which is why repeated concepts are the most efficient thing to practise.

Question	What it asks	Answer
CAT 2024 Slot 2 · QA Q16	1/α^2 + 1/β^2 = 15; find (α^3 + β^3)^2	C
CAT 2023 Slot 3 · QA Q5	difference and squares of reciprocals of roots	9
CAT 2017 Slot 2 · QA Q24	minimise sum of squares of roots over a parameter	C
CAT 2023 Slot 1 · QA Q6	sum and product of roots are roots of another quadratic	6
CAT 2019 Slot 2 · QA Q25	roots 4a and 3a; possible value of b^2 + c	B

Part of Equations (52 questions since 2017).