Location of roots

Location of roots Quiz

Spec 6.1 · Edexcel International A Level Maths: Quiz

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  1. 1. f(x)=x2−5f(x)=x^2-5. In which interval does f(x)=0f(x)=0 have a root?

    • A. [0,1][0,1]
    • B. [1,2][1,2]
    • C. [2,3][2,3]
    • D. [3,4][3,4]

  2. 2. For f(x)=1xf(x)=\frac1x, f(−1)=−1f(-1)=-1 and f(1)=1f(1)=1. Why is there no root in [−1,1][-1,1]?

    • A. ff is not continuous at x=0x=0
    • B. f(−1)f(-1) and f(1)f(1) have opposite signs
    • C. ff is a polynomial
    • D. f(0)=0f(0)=0

  3. 3. f(x)=(x−2)2f(x)=(x-2)^2 has f(1)=1f(1)=1 and f(3)=1f(3)=1. What does this show?

    • A. There is no root in [1,3][1,3]
    • B. There are two roots in [1,3][1,3]
    • C. ff is not continuous
    • D. Equal signs at the ends do not rule out a root in between

  4. 4. f(x)=x3−x−1f(x)=x^3-x-1 has f(1.2)=−0.472f(1.2)=-0.472, f(1.3)=−0.103f(1.3)=-0.103 and f(1.4)=0.344f(1.4)=0.344. In which interval is the root?

    • A. [1.2,1.3][1.2,1.3]
    • B. [1.3,1.4][1.3,1.4]
    • C. [1.4,1.5][1.4,1.5]
    • D. [1.1,1.2][1.1,1.2]

  5. 5. Which statement is needed in a full answer that a root lies in [a,b][a,b]?

    • A. f(a)=f(b)f(a)=f(b)
    • B. f′(x)>0f'(x)>0
    • C. ff is continuous and f(a)f(a), f(b)f(b) have opposite signs
    • D. f(a)>0f(a)>0 and f(b)>0f(b)>0

Quiz