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Solve a cubic equation when one root is known

11th grade (Year 12 in England) · 16 questions · Common Core: HSA.APR.B.3, HSN.CN.C.9 · England: A-level Pure Mathematics

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  1. Question 1

    x = 1 is a solution of x³ + 2x² − 3x = 0. Find all the solutions, separated by commas.

    x =

  2. Question 2

    Solve x³ + x² − 6x = 0. Give all the solutions, separated by commas.

    x =

  3. Question 3

    x = 5 is a solution of x³ − 11x² + 38x − 40 = 0. Find all the solutions, separated by commas.

    x =

  4. Question 4

    Solve x³ − 2x² − 8x = 0. Give all the solutions, separated by commas.

    x =

  5. Question 5

    x = 3 is a solution of x³ − x² − 6x = 0. Find all the solutions, separated by commas.

    x =

  6. Question 6

    Solve x³ + 4x² − 12x = 0. Give all the solutions, separated by commas.

    x =

  7. Question 7

    x = −1 is a solution of x³ + 5x² − x − 5 = 0. Find all the solutions, separated by commas.

    x =

  8. Question 8

    Solve x³ − 4x² + 3x = 0. Give all the solutions, separated by commas.

    x =

  9. Question 9

    x = 0 is a solution of x³ − 4x = 0. Find all the solutions, separated by commas.

    x =

  10. Question 10

    Solve x³ − 10x² + 24x = 0. Give all the solutions, separated by commas.

    x =

  11. Question 11

    x = 3 is a solution of x³ + 3x² − 13x − 15 = 0. Find all the solutions, separated by commas.

    x =

  12. Question 12

    Solve x³ + 6x² + 5x = 0. Give all the solutions, separated by commas.

    x =

  13. Question 13

    x = 4 is a solution of x³ − 2x² − 11x + 12 = 0. Find all the solutions, separated by commas.

    x =

  14. Question 14

    Solve x³ + 2x² − 3x = 0. Give all the solutions, separated by commas.

    x =

  15. Question 15

    x = 4 is a solution of x³ − 3x² − 16x + 48 = 0. Find all the solutions, separated by commas.

    x =

  16. Question 16

    Solve x³ − 2x² − 3x = 0. Give all the solutions, separated by commas.

    x =

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Answer key: Solve a cubic equation when one root is known

  1. 1. x = -3 or x = 0 or x = 1

  2. 2. x = -3 or x = 0 or x = 2

  3. 3. x = 2 or x = 4 or x = 5

  4. 4. x = -2 or x = 0 or x = 4

  5. 5. x = -2 or x = 0 or x = 3

  6. 6. x = -6 or x = 0 or x = 2

  7. 7. x = -5 or x = -1 or x = 1

  8. 8. x = 0 or x = 1 or x = 3

  9. 9. x = -2 or x = 0 or x = 2

  10. 10. x = 0 or x = 4 or x = 6

  11. 11. x = -5 or x = -1 or x = 3

  12. 12. x = -5 or x = -1 or x = 0

  13. 13. x = -3 or x = 1 or x = 4

  14. 14. x = -3 or x = 0 or x = 1

  15. 15. x = -4 or x = 3 or x = 4

  16. 16. x = -1 or x = 0 or x = 3