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How do I decide whether I need to take the positive or negative root of b^2?

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    part ii
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    if in doubt take the + version
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    (Original post by the bear)
    if in doubt take the + version
    but why would the negative one not work and how would you know
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    (Original post by KloppOClock)
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    It doesn't matter. Just pick a value of b, then get your value of a^2 and pick a value of a (expression will look the same up to order of the factors regardless of a's sign of course). It will be a correct factorisation if your expressions are correct.
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    (Original post by KloppOClock)
    but why would the negative one not work and how would you know
    So essentially, it would work. Think about it. You know that whenever your equations for A and B in terms of a and b hold, the factorisation is correct. Ergo so long as a and b are such that these equations hold, everything's fine.
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    (Original post by 13 1 20 8 42)
    So essentially, it would work. Think about it. You know that whenever your equations for A and B in terms of a and b hold, the factorisation is correct. Ergo so long as a and b are such that these equations hold, everything's fine.
    but i got different values of A and B tho
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    (Original post by KloppOClock)
    but i got different values of A and B tho
    I'm not sure what you mean..
    I presume you have got to the point where you have, for the general case, two equations, I believe they were A = 2b - a^2 and B = b^2.
    In this specific case, your A is -20, and your B is 16.
    Therefore you simply need to find some a and b such that 16 = b^2 and -20 = 2b - a^2. So long as a and b satisfy these equations, you're fine. So for instance you could decide to pick b = -4, and then a^2 = 2b + 20 = 12, and you could pick a = root(12) (i.e. the positive root). The resulting factorisation will be correct. You could have picked b = 4 to begin with, or you could have picked a = -root(12) after picking b = -4, it all makes no difference.
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    (Original post by 13 1 20 8 42)
    I'm not sure what you mean..
    I presume you have got to the point where you have, for the general case, two equations, I believe they were A = 2b - a^2 and B = b^2.
    In this specific case, your A is -20, and your B is 16.
    Therefore you simply need to find some a and b such that 16 = b^2 and -20 = 2b - a^2. So long as a and b satisfy these equations, you're fine. So for instance you could decide to pick b = -4, and then a^2 = 2b + 20 = 12, and you could pick a = root(12) (i.e. the positive root). The resulting factorisation will be correct. You could have picked b = 4 to begin with, or you could have picked a = -root(12) after picking b = -4, it all makes no difference.
    but root 12 isnt a correct answer, they only used the positive root of b to get root 28
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    (Original post by 13 1 20 8 42)
    I'm not sure what you mean..
    I presume you have got to the point where you have, for the general case, two equations, I believe they were A = 2b - a^2 and B = b^2.
    In this specific case, your A is -20, and your B is 16.
    Therefore you simply need to find some a and b such that 16 = b^2 and -20 = 2b - a^2. So long as a and b satisfy these equations, you're fine. So for instance you could decide to pick b = -4, and then a^2 = 2b + 20 = 12, and you could pick a = root(12) (i.e. the positive root). The resulting factorisation will be correct. You could have picked b = 4 to begin with, or you could have picked a = -root(12) after picking b = -4, it all makes no difference.
    okay i get you now, both of my solutions are correct, but when i was typing it in an online expand calculator i was typing it in wrong. the only problem I have is that the mark scheme only states the factorisation with the root28 as the correct answer and omits the answer with root12; would you get the marks if you just did the root 12 factorisation?
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    (Original post by KloppOClock)
    okay i get you now, both of my solutions are correct, but when i was typing it in an online expand calculator i was typing it in wrong. the only problem I have is that the mark scheme only states the factorisation with the root28 as the correct answer and omits the answer with root12; would you get the marks if you just did the root 12 factorisation?
    Well, presumably they just omitted it as they assumed most people would go with the positive root. I mean, think about this logically. It says "use this information to find a factorisation of *equation*". Going by the information you have, it is perfectly reasonable to find the factorisation involving root(12), and it would be utterly absurd for you not to get marks for it.
 
 
 
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