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    I'm a bit confused about why the answer to this inequality turns out as it does:

    Find the range of values for k for which the equation x^2 - kx + (k + 3) = 0

    My working:

    b^2 - 4ac > 0
    k^2 - 4k - 12 > 0
    (k - 6)(k + 2) > 0
    so critical points are at x = -2 and x = 6

    I draw the graph, and see when the graph of this quadratic is above 0.

    Which is when k < -2 or x > 6.

    But the answer is -2 < k < 6?
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    Did the question ask for the range of values where the equation has roots, or where it doesn't?
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    (Original post by UCASLord)
    I'm a bit confused about why the answer to this inequality turns out as it does:

    Find the range of values for k for which the equation x^2 - kx + (k + 3) = 0

    My working:

    b^2 - 4ac > 0
    k^2 - 4k - 12 > 0
    (k - 6)(k + 2) > 0
    so critical points are at x = -2 and x = 6

    I draw the graph, and see when the graph of this quadratic is above 0.

    Which is when k < -2 or x > 6.

    But the answer is -2 < k < 6?
    check that you've read the question properly. That interval contains the values of k for which there are no real roots.
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    (Original post by _gcx)
    check that you've read the question properly. That interval contains the values of k for which there are no real roots.
    I know - that's why I created this thread.

    I've definitely read this question properly.

    It's question 4a) in the Edexcel C1 textbook, section 3.

    At first, I thought it was a textbook error, but question 4b) also gives the interval for which the values of k have no read roots, which is very confusing.
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    (Original post by UCASLord)
    I know - that's why I created this thread.

    I've definitely read this question properly.

    It's question 4a) in the Edexcel C1 textbook, section 3.

    At first, I thought it was a textbook error, but question 4b) also gives the interval for which the values of k have no read roots, which is very confusing.
    you mean they gave the same interval for a) and b)? Then I'd suggest an error in the textbook.
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    (Original post by DFranklin)
    Did the question ask for the range of values where the equation has roots, or where it doesn't?
    Hey Franklin, missed your reply at first.

    It's question 4a) from the Edexcel C1 textbook, section 3. I'm sure I read the question correctly.
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    (Original post by _gcx)
    you mean they gave the same interval for a) and b)? Then I'd suggest an error in the textbook.
    Oh no, sorry. They also gave an interval where k has no real roots, but asked for where k does have real roots. So it's the same logical error (if it is indeed a textbook error...)

    Edit: The constant is "p" in the next question.
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    Note that it's obvious the equation has no roots when k=0.
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    (Original post by UCASLord)
    Hey Franklin, missed your reply at first.

    It's question 4a) from the Edexcel C1 textbook, section 3. I'm sure I read the question correctly.
    I think I have a digital copy of this actually, I'll have a look. What page is it exactly?
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    (Original post by DFranklin)
    Note that it's obvious the equation has no roots when k=0.
    Well spotted, because then 3 = 0, which is not true, and yet 0 is within the range of solutions given in the answer section.

    I guess the writer must have been a bit tired on the day :P
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    (Original post by UCASLord)
    Well spotted, because then 3 = 0, which is not true, and yet 0 is within the range of solutions given in the answer section.

    I guess the writer must have been a bit tired on the day :P
    Well, not quite, you'd have x^2 + 3 = 0 , which has no real solutions.
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    (Original post by UCASLord)
    I'm a bit confused about why the answer to this inequality turns out as it does:

    Find the range of values for k for which the equation x^2 - kx + (k + 3) = 0

    My working:

    b^2 - 4ac > 0
    k^2 - 4k - 12 > 0
    (k - 6)(k + 2) > 0
    so critical points are at x = -2 and x = 6

    I draw the graph, and see when the graph of this quadratic is above 0.

    Which is when k < -2 or x > 6.

    But the answer is -2 < k < 6?
    It's a typo that I think might have been corrected in later editions of the textbook. Here's the correct version that is in the Solutionbank:

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    (Original post by Notnek)
    It's a typo that I think might have been corrected in later editions of the textbook. Here's the correct version that is in the Solutionbank:

    That's it! I can see the difference in a) in my copy of the textbook, it says "has real roots." Finally, a time where the textbook is wrong for real. xD

    I think I still misunderstood part b), though :P
 
 
 
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