Answer: -(b³ - 3abc)/a³.
- A (3abc - b³)/a³
- B -(b³ - 3abc)/a³
- C (b³ - 3abc)/a³
- D 3abc/a³
Correct answer: B. -(b³ - 3abc)/a³
Explanation: Vieta's formulas: α+β = -b/a, αβ = c/a. Use identity: α³+β³ = (α+β)³ - 3αβ(α+β) = (-b/a)³ - 3(c/a)(-b/a) = -b³/a³ + 3bc/a². Common denominator a³ gives (-b³ + 3abc)/a³ = -(b³ - 3abc)/a³. Answer: -(b³ - 3abc)/a³
A complex number z = a+ib is plotted as a point (or vector from the origin) on the Argand plane, with the real part along the horizontal axis and the imaginary part along the vertical; its modulus |z| is the vector's length, and its argument θ is the angle from the positive real axis.
Concept context
Complex numbers in a+ib form, modulus, argument, polar form, cube roots of unity, and quadratic equations with complex roots
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