1-5 The discriminant and the nature of the two roots
Point 5 of 11 — Unit 1: Complex Numbers, the Quadratic Equation, Sign of a Function and Quadratic InequalitiesQuestion bank: 0 questions (0 with pictures)
05 1-5 The discriminant and the nature of the two roots
Δ > 0: two different real roots.
Δ = 0: two equal real roots, x = −b/(2a).
Δ < 0: no real roots; the two roots are conjugate imaginary numbers.
If a, b, c are rational: Δ > 0 and Δ aperfect square → two differentrationalroots; Δ > 0 but not a perfect square → two different irrationalroots.
Perfect squares to recognise at once: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 …
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