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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 − 4 = 0. Give exact answers in the form (p ± √q)/r.

    • A. x = (6 ± √52)/2
    • B. x = (−6 ± √52)/2
    • C. x = (6 ± √52)/1
    • D. x = 6 ± √52/2

  2. Question 2

    Solve x² + 2x − 19 = 0 with the quadratic formula. Simplify fully.

    • A. x = −1 ± 4√5
    • B. x = 1 ± 2√5
    • C. x = −1 ± √20/2
    • D. x = −1 ± 2√5

  3. Question 3

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

    • A. x = (−3 ± √45)/6
    • B. x = 3 ± √45/6
    • C. x = (3 ± √45)/3
    • D. x = (3 ± √45)/6

  4. Question 4

    Solve x² − 10x − 3 = 0 with the quadratic formula. Simplify fully.

    • A. x = 5 ± 2√7
    • B. x = 5 ± 4√7
    • C. x = −5 ± 2√7
    • D. x = 10 ± 2√7

  5. Question 5

    Solve 2x² + 7x + 1 = 0. Give exact answers in the form (p ± √q)/r.

    • A. x = −7 ± √41/4
    • B. x = (−7 ± √57)/4
    • C. x = (7 ± √41)/4
    • D. x = (−7 ± √41)/4

  6. Question 6

    Solve x² + 10x − 3 = 0 with the quadratic formula. Simplify fully.

    • A. x = −5 ± √28/2
    • B. x = 5 ± 2√7
    • C. x = −5 ± 2√7
    • D. x = −5 ± 4√7

  7. Question 7

    Solve 2x² + 8x + 5 = 0. Give exact answers in the form (p ± √q)/r.

    • A. x = (−8 ± √24)/4
    • B. x = −8 ± √24/4
    • C. x = (−8 ± √24)/2
    • D. x = (8 ± √24)/4

  8. Question 8

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

    • A. x = −1 ± 4√6
    • B. x = −1 ± 2√6
    • C. x = −2 ± 2√6
    • D. x = −1 ± √24/2

  9. Question 9

    Solve 3x² + 5x + 1 = 0. Give exact answers in the form (p ± √q)/r.

    • A. x = (5 ± √13)/6
    • B. x = (−5 ± √13)/3
    • C. x = (−5 ± √37)/6
    • D. x = (−5 ± √13)/6

  10. Question 10

    Solve x² + 4x − 23 = 0 with the quadratic formula. Simplify fully.

    • A. x = 2 ± 3√3
    • B. x = −2 ± 3√3
    • C. x = −2 ± √27/2
    • D. x = −4 ± 3√3

  11. Question 11

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

    • A. x = (−6 ± √108)/6
    • B. x = −6 ± √108/6
    • C. x = (−6 ± √108)/3
    • D. x = (6 ± √108)/6

  12. Question 12

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

    • A. x = 3 ± 2√3
    • B. x = −3 ± 2√3
    • C. x = 3 ± √12/2
    • D. x = 6 ± 2√3

  13. Question 13

    Solve x² − 4x − 3 = 0. Give exact answers in the form (p ± √q)/r.

    • A. x = (4 ± √28)/2
    • B. x = 4 ± √28/2
    • C. x = (−4 ± √28)/2
    • D. x = (4 ± √4)/2

  14. Question 14

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

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

  15. Question 15

    Solve 3x² + 8x + 2 = 0. Give exact answers in the form (p ± √q)/r.

    • A. x = (8 ± √40)/6
    • B. x = −8 ± √40/6
    • C. x = (−8 ± √40)/3
    • D. x = (−8 ± √40)/6

  16. Question 16

    Solve x² + 4x − 14 = 0 with the quadratic formula. Simplify fully.

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

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Answer key: Give exact solutions with the quadratic formula

  1. 1. A. x = (6 ± √52)/2

  2. 2. D. x = −1 ± 2√5

  3. 3. D. x = (3 ± √45)/6

  4. 4. A. x = 5 ± 2√7

  5. 5. D. x = (−7 ± √41)/4

  6. 6. C. x = −5 ± 2√7

  7. 7. A. x = (−8 ± √24)/4

  8. 8. B. x = −1 ± 2√6

  9. 9. D. x = (−5 ± √13)/6

  10. 10. B. x = −2 ± 3√3

  11. 11. A. x = (−6 ± √108)/6

  12. 12. A. x = 3 ± 2√3

  13. 13. A. x = (4 ± √28)/2

  14. 14. B. x = 4 ± 2√7

  15. 15. D. x = (−8 ± √40)/6

  16. 16. B. x = −2 ± 3√2