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    Not sure if this is step level or below Its just one of the prep questions I am meant to do before my step class and I cant figure it out.

    question 16
    find the real values of K for which the equation x^2+ (k+1) +k^2=0 has
    A real roots, B, one root is double the other.

    part A is is easy that is just using the discriminant and then drawing a graph and stating the values of the inequalities of X.

    K is => -1/3 or K is =<1

    I successfully got that part rather quickly but I cant figure out how to proceed to do part B

    I mean I know that in terms of roots A+B= -b/a and since a is 1 A+B=-b

    I get that. I also get that root A * root B = c/a which again since a is 1 just gives K2

    but I don't know where to go from here.

    I mean I tried putting this into a quadratic inbetween inequalities which got messy and nowhere.

    I mean having -1/3<=(-(k+1)+-root(-3k^2+2k+1))<= 1 does not seem like I am doing this right might have made a mistake somewhere too but I have a strong feeling this is not the right method.

    Help
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    oh and I am aware that if A+B= -b and one root is twice the other then A+2A= -b would give 3a= -b

    but have not managed to find a way of using that.
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    (Original post by Luke7456)
    ..
    If the roots are R and 2R, then the sum of the roots is 3R and the product of the roots is 2R^2. This is enough to find k.

    Also, don't post maths problems in this forum, as the sticky says:

    (Original post by DFranklin)
    This University Mathematics forum is for discussion of mathematics that is specifically to do with studying at university.

    That is, for questions like "Do you think I would enjoy a Maths degree", or "Should I apply to Warwick or Imperial?", or "Is it possible to change to maths from physics after one year?".

    It is not for questions like "How do you integrate exp(-x^2)?". The correct forum for those questions is the Maths Forum that is part of the "Study Help" set of forums.
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    (Original post by Luke7456)
    Not sure if this is step level or below Its just one of the prep questions I am meant to do before my step class and I cant figure it out.

    question 16
    find the real values of K for which the equation x^2+ (k+1) +k^2=0 has
    A real roots, B, one root is double the other.

    part A is is easy that is just using the discriminant and then drawing a graph and stating the values of the inequalities of X.

    K is => -1/3 or K is =<1

    I successfully got that part rather quickly but I cant figure out how to proceed to do part B

    I mean I know that in terms of roots A+B= -b/a and since a is 1 A+B=-b

    I get that. I also get that root A * root B = c/a which again since a is 1 just gives K2

    but I don't know where to go from here.

    I mean I tried putting this into a quadratic inbetween inequalities which got messy and nowhere.

    I mean having -1/3<=(-(k+1)+-root(-3k^2+2k+1))<= 1 does not seem like I am doing this right might have made a mistake somewhere too but I have a strong feeling this is not the right method.

    Help
     k = \frac{2}{7} - \frac{3}{7} \sqrt{2}

    Attachment 675796
 
 
 
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