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Thread: halving the interval

  1. #1
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    halving the interval

    f(x) = x^3 + 5x^2 + 17x - 10.
    The equation f(x) = 0 has only one real root.

    i. Show the root lies between 0 and 2

    ii. use one application of 'halving the interval' to find a smaller interval

    iii. Which end of the smaller interval found in ii. is closer to the root? Why?

    for i. i got
    P(0) = -10 -neg
    P(2) = 52 -pos
    therefore the root lies between 0 and 2

    ii. P(1) = 13 -pos
    therefore the root lies between 0 and 1

    are these right??
    how do you do iii.?
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  2. #2
    ynj
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    Quote Originally Posted by deej813 View Post
    f(x) = x^3 + 5x^2 + 17x - 10.
    The equation f(x) = 0 has only one real root.

    i. Show the root lies between 0 and 2

    ii. use one application of 'halving the interval' to find a smaller interval

    iii. Which end of the smaller interval found in ii. is closer to the root? Why?

    for i. i got
    P(0) = -10 -neg
    P(2) = 52 -pos
    therefore the root lies between 0 and 2

    ii. P(1) = 13 -pos
    therefore the root lies between 0 and 1

    are these right??
    how do you do iii.?
    P(0.5)<0,so the root is greater than 0.5, then 1 is nearer..
    i,ii are right.
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  3. #3
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    ok thanks
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