4.05a-c Relationships between roots and coefficients; partial fractions Quiz: OCR Further Maths, Unit 1

The 20 questions

1. What is the sum of the roots of the quadratic equation ax^2 + bx + c = 0?

   • b/a
   • -c/a
   • -b/a
   • c/a

2. What is the product of the roots of the quadratic equation ax^2 + bx + c = 0?

   • b/a
   • c/a
   • -c/a
   • -b/a

3. For the cubic ax^3 + bx^2 + cx + d = 0, what is the value of sum alpha?

   • b/a
   • -d/a
   • c/a
   • -b/a

4. For ax^3 + bx^2 + cx + d = 0, what is the value of sum alpha beta?

   • c/a
   • -c/a
   • -d/a
   • d/a

5. What is the product of all three roots of ax^3 + bx^2 + cx + d = 0?

   • -c/a
   • -d/a
   • c/a
   • d/a

6. For ax^4 + bx^3 + cx^2 + dx + e = 0, what is the product of all four roots?

   • e/a
   • d/a
   • -e/a
   • -d/a

7. What is the correct partial fraction form for 1 over (x - 1)^2 (x + 2)?

   • A/(x-1)^2 + B/(x+2)
   • A/(x-1) + B/(x-1)^2 + C/(x+2)
   • A/(x-1) + B/(x+2)
   • A/(x-1) + Bx/(x-1)^2 + C/(x+2)

8. What is the numerator form over x^2 + 4 when finding partial fractions?

   • A
   • Ax^2 + B
   • Ax + B
   • A/(x^2 + 4)

9. What is the sum of the roots of 2x^2 - 8x + 5 = 0?

   • -4
   • -5/2
   • 5/2
   • 4

10. What is the product of the roots of 3x^2 + 6x - 12 = 0?

    • -4
    • 2
    • 4
    • -2

11. What is the sum of the roots of the cubic x^3 - 6x^2 + 11x - 6 = 0?

    • -6
    • -11
    • 11
    • 6

12. What is the product of the roots of x^3 + 2x^2 - 5x - 8 = 0?

    • -8
    • 5
    • -5
    • 8

13. If roots of x^2 - 5x + 6 = 0 are doubled, what is the new sum of roots?

    • 5
    • 12
    • 20
    • 10

14. In 5/(x - 1)(x + 4) = A/(x - 1) + B/(x + 4), what is the value of A?

    • 1
    • -1
    • 5
    • 5/4

15. In 3/(x + 2)(x - 1) = A/(x + 2) + B/(x - 1), what is the value of B?

    • -1
    • 1
    • -3
    • 3

16. What is the sum of the roots of 2x^4 - 10x^3 + 3x + 7 = 0?

    • 5
    • -7/2
    • 7/2
    • -5

17. If roots of x^2 - 4x + 2 = 0 are alpha and beta, what is alpha^2 + beta^2?

    • 8
    • 20
    • 16
    • 12

18. For x^2 - 6x + 3 = 0, what is 1/alpha + 1/beta?

    • 1/2
    • -2
    • 6
    • 2

19. For x^3 - 3x + 1 = 0, substitute x = y - 1 to find the y^2 coefficient.

    • -3
    • 0
    • 3
    • -1

20. What polynomial term is produced when performing partial fractions on (x^2 + 1)/(x^2 - 1)?

    • x
    • x + 1
    • 0
    • 1

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