The discriminant
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All 9 Flashcards — The discriminant
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Question
What is the discriminant?
Answer
Δ = b² − 4ac — the expression under the root in the quadratic formula.
Question
What does Δ > 0 mean?
Answer
Two distinct real roots; the graph cuts the x-axis twice.
Question
What does Δ = 0 mean?
Answer
One repeated real root; the graph touches the x-axis (tangent).
Question
What does Δ < 0 mean?
Answer
No real roots; the graph misses the x-axis.
Question
How do you set up a tangency problem?
Answer
Set line = curve, form a quadratic = 0, then set Δ = 0 (one intersection).
Question
'Equal roots' translates to which condition?
Answer
Δ = 0.
Question
'No real roots' translates to which condition?
Answer
Δ < 0.
Question
x² + kx + 9 = 0 has equal roots. Find k > 0.
Answer
Δ = k² − 36 = 0 ⇒ k = 6.
Question
Do you need to solve the quadratic to count its roots?
Answer
No — just compute Δ and read its sign.
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Topic 2.7 hub
Quadratic equations & discriminant
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