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Math Help - check work 3

  1. #1
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    check work 3

    1. which of the following statements are true for f(x)=-2(x-1)(x-2)(x+3)

    i) as x-> infinity, f(x)-> -infinity
    ii) as x-> infinity, f(x)-> infinity
    iii) as x-> -infinity, f(x)-> -infinity
    iv) as x-> -infinity,f(x)-> infinity

    a) i and iv
    b) i and ii
    c) i
    d) i and iii

    my choice: d)

    2. which statement is true

    a) a degree 4 function may have no real zero
    b) a degree 4 function may have 1 or 2 real zeros
    c) a degree 4 function may have 3 or 4 real zeros
    d) all of the above

    my choice: c)
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  2. #2
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    Quote Originally Posted by william View Post
    1. which of the following statements are true for f(x)=-2(x-1)(x-2)(x+3)

    i) as x-> infinity, f(x)-> -infinity
    ii) as x-> infinity, f(x)-> infinity
    iii) as x-> -infinity, f(x)-> -infinity
    iv) as x-> -infinity,f(x)-> infinity

    a) i and iv
    b) i and ii
    c) i
    d) i and iii

    my choice: d)

    2. which statement is true

    a) a degree 4 function may have no real zero
    b) a degree 4 function may have 1 or 2 real zeros
    c) a degree 4 function may have 3 or 4 real zeros
    d) all of the above

    my choice: c)
    d would be true of the equation didn't have a minus sign in the beginning. But it does. So it's a.

    All of the above are true for 2.
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  3. #3
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    Quote Originally Posted by william View Post
    1. which of the following statements are true for f(x)=-2(x-1)(x-2)(x+3)

    i) as x-> infinity, f(x)-> -infinity
    ii) as x-> infinity, f(x)-> infinity
    iii) as x-> -infinity, f(x)-> -infinity
    iv) as x-> -infinity,f(x)-> infinity

    a) i and iv
    b) i and ii
    c) i
    d) i and iii

    my choice: d) <-WRONG the answer is a)

    2. which statement is true

    a) a degree 4 function may have no real zero
    b) a degree 4 function may have 1 or 2 real zeros
    c) a degree 4 function may have 3 or 4 real zeros
    d) all of the above

    my choice: c) <- WRONG I think they want answer d)
    For Q2:
    Any quartic can either have:

    4 real roots -> quartic expressible in terms of a product of 4 linear factors

    2 real roots -> quartic expressible in terms of a product of quadratic (with no real roots) and 2 linear factors

    no real roots -> quartic expressible in terms of a product of 2 quadratic factors (with no real roots).
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