Discriminant conditions for real, distinct or no real roots

CAT has tested this idea 6 times across 6 papers, from 2017 to 2022. 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 2022 Slot 3 · QA Q1	one equation no real roots, other two distinct	C
CAT 2020 Slot 3 · QA Q23	both quadratics have real roots; minimise m + n	B
CAT 2017 Slot 1 · QA Q27	largest n for two distinct real roots	24
CAT 2019 Slot 2 · QA Q13	real distinct roots iff condition on log A	C
CAT 2018 Slot 2 · QA Q23	quadratics positive for all x; maximise 2a − 6b	36
CAT 2022 Slot 1 · QA Q5	b^2 < 4ac means f has constant sign	B

Part of Equations (52 questions since 2017).