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Flip to reveal answersSum and product of roots of ax² + bx + c = 0?
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All 8 Flashcards — Sum & product of roots
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Question
Sum and product of roots of ax² + bx + c = 0?
Answer
Sum = −b/a, product = c/a.
Question
General sum and product of roots of a degree-n polynomial?
Answer
Sum = −aₙ₋₁/aₙ; product = (−1)ⁿ a₀/aₙ.
Question
Cubic ax³ + bx² + cx + d: sum and product of roots?
Answer
Sum = −b/a; product = −d/a (the (−1)³ makes it negative).
Question
Why use sum/product instead of solving?
Answer
It reads the symmetric functions of the roots straight off the coefficients — no need to find the roots.
Question
Roots of 2x² − 6x + 1 = 0: sum and product?
Answer
Sum = 6/2 = 3, product = 1/2.
Question
Roots of x³ − 4x² + x + 6 = 0: sum and product?
Answer
Sum = 4, product = −6.
Question
Does the product of roots change sign with degree?
Answer
Yes — it's (−1)ⁿ a₀/aₙ, so + for even degree, − for odd.
Question
Roots of x² − kx + (k+3) = 0 sum to 5 — find k.
Answer
Sum = k = 5.
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Full study notes for Sum & product of roots
Topic 2.12 hub
Factor & remainder (HL only)
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