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Equations and Inequalities – Relationship Between Roots and Coefficients of Cubic Equations (Challenge)

Exams by Grade · K10 · Author: jaeinpark

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  1. Q1
    When the solutions of the cubic equation are three consecutive integers, find the value of for the constants and .
  2. Q2
    When the ratio of the solutions of the cubic equation is , find the value of for the constants and .
  3. Q3
    When the solutions of the quadratic equation are also the solutions of the cubic equation , find the value of for the constants and .
  4. Q4
    When and are the solutions of the cubic equation , find the value of .
  5. Q5
    The volume of a cone with the radius and height is equal to the volume of a cylinder with the radius and the height . Find the value of .
  6. Q6
    The length and width of a cube were increased by and , respectively, and the height was reduced to times to create a new cuboid. If the volume of the cuboid is times the volume of the cube, what is the length of an edge of the original cube?