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Give exact solutions with the quadratic formula

10th grade (Year 11 in England) · 16 questions · Common Core: HSA.REI.B.4.B · England: GCSE Higher Algebra

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  1. Question 1

    Solve x² + 6x − 18 = 0 with the quadratic formula. Simplify fully.

    • A. x = −3 ± 3√3
    • B. x = −3 ± 6√3
    • C. x = −3 ± √27/2
    • D. x = 3 ± 3√3

  2. Question 2

    Solve 2x² − 9x + 6 = 0. Give exact answers in the form (p ± √q)/r.

    • A. x = (−9 ± √33)/4
    • B. x = (9 ± √33)/2
    • C. x = (9 ± √33)/4
    • D. x = 9 ± √33/4

  3. Question 3

    Solve x² + 6x − 9 = 0 with the quadratic formula. Simplify fully.

    • A. x = −3 ± 3√2
    • B. x = −3 ± 6√2
    • C. x = −6 ± 3√2
    • D. x = −3 ± √18/2

  4. Question 4

    Solve 2x² − 5x − 2 = 0. Give exact answers in the form (p ± √q)/r.

    • A. x = (5 ± √9)/4
    • B. x = (5 ± √41)/4
    • C. x = (−5 ± √41)/4
    • D. x = (5 ± √41)/2

  5. Question 5

    Solve x² − 8x − 12 = 0 with the quadratic formula. Simplify fully.

    • A. x = 4 ± 2√7
    • B. x = 8 ± 2√7
    • C. x = 4 ± √28/2
    • D. x = 4 ± 4√7

  6. Question 6

    Solve 2x² + 7x − 7 = 0. Give exact answers in the form (p ± √q)/r.

    • A. x = (−7 ± √105)/2
    • B. x = −7 ± √105/4
    • C. x = (7 ± √105)/4
    • D. x = (−7 ± √105)/4

  7. Question 7

    Solve x² + 2x − 23 = 0 with the quadratic formula. Simplify fully.

    • A. x = −1 ± 2√6
    • B. x = −2 ± 2√6
    • C. x = −1 ± 4√6
    • D. x = 1 ± 2√6

  8. Question 8

    Solve 2x² + 6x − 3 = 0. Give exact answers in the form (p ± √q)/r.

    • A. x = (−6 ± √12)/4
    • B. x = −6 ± √60/4
    • C. x = (6 ± √60)/4
    • D. x = (−6 ± √60)/4

  9. Question 9

    Solve x² − 6x − 3 = 0 with the quadratic formula. Simplify fully.

    • A. x = 3 ± √12/2
    • B. x = 3 ± 4√3
    • C. x = −3 ± 2√3
    • D. x = 3 ± 2√3

  10. Question 10

    Solve x² + 7x + 4 = 0. Give exact answers in the form (p ± √q)/r.

    • A. x = (−7 ± √33)/2
    • B. x = (7 ± √33)/2
    • C. x = (−7 ± √65)/2
    • D. x = (−7 ± √33)/1

  11. Question 11

    Solve x² − 8x + 8 = 0 with the quadratic formula. Simplify fully.

    • A. x = 8 ± 2√2
    • B. x = 4 ± 4√2
    • C. x = 4 ± √8/2
    • D. x = 4 ± 2√2

  12. Question 12

    Solve 2x² − 7x − 2 = 0. Give exact answers in the form (p ± √q)/r.

    • A. x = (7 ± √33)/4
    • B. x = (7 ± √65)/4
    • C. x = (7 ± √65)/2
    • D. x = (−7 ± √65)/4

  13. Question 13

    Solve x² + 2x − 27 = 0 with the quadratic formula. Simplify fully.

    • A. x = 1 ± 2√7
    • B. x = −1 ± 2√7
    • C. x = −1 ± 4√7
    • D. x = −2 ± 2√7

  14. Question 14

    Solve x² − 9x − 1 = 0. Give exact answers in the form (p ± √q)/r.

    • A. x = (9 ± √77)/2
    • B. x = (9 ± √85)/2
    • C. x = 9 ± √85/2
    • D. x = (−9 ± √85)/2

  15. Question 15

    Solve x² − 8x − 2 = 0 with the quadratic formula. Simplify fully.

    • A. x = 4 ± 6√2
    • B. x = 4 ± √18/2
    • C. x = 8 ± 3√2
    • D. x = 4 ± 3√2

  16. Question 16

    Solve x² − 7x + 8 = 0. Give exact answers in the form (p ± √q)/r.

    • A. x = (7 ± √81)/2
    • B. x = (−7 ± √17)/2
    • C. x = (7 ± √17)/1
    • D. x = (7 ± √17)/2

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  1. x = −3 ± 3√3
  2. x = (9 ± √33)/4
  3. x = −3 ± 3√2
  4. x = (5 ± √41)/4
  5. x = 4 ± 2√7
  6. x = (−7 ± √105)/4
  7. x = −1 ± 2√6
  8. x = (−6 ± √60)/4
  9. x = 3 ± 2√3
  10. x = (−7 ± √33)/2
  11. x = 4 ± 2√2
  12. x = (7 ± √65)/4
  13. x = −1 ± 2√7
  14. x = (9 ± √85)/2
  15. x = 4 ± 3√2
  16. x = (7 ± √17)/2