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    Any help would be greatly appreciated. I am ok with parts i and ii of this question, but part iii is really driving me crazy.

    Given that
    X^2 +4x +c = (x + a )^2 + b
    Where a, b and c are constants
    (i) Find the value of a

    x^2 +4x +c = (x + a )^2 + b = x^2 + 2ax + a^2 + b
    Gathering together like terms,
    4x = 2ax
    Therefore
    4 = 2a
    Therefore
    a = 2
    (ii) Find b in terms of c

    c = a^2 + b = 2x2 +b = 4 + b

    therefore

    c -4 = b

    And here is the bit that I am stuck on......

    (iii) Given also that the equation X^2 +4x +c = 0 has unequal real roots, find the range of possible values of c.

    The answer is c < 4, but I have no idea how that was arrived at
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    (Original post by apsley)
    Any help would be greatly appreciated. I am ok with parts i and ii of this question, but part iii is really driving me crazy.

    Given that
    X^2 +4x +c = (x + a )^2 + b
    Where a, b and c are constants
    (i) Find the value of a

    x^2 +4x +c = (x + a )^2 + b = x^2 + 2ax + a^2 + b
    Gathering together like terms,
    4x = 2ax
    Therefore
    4 = 2a
    Therefore
    a = 2
    (ii) Find b in terms of c

    c = a^2 + b = 2x2 +b = 4 + b

    therefore

    c -4 = b

    And here is the bit that I am stuck on......

    (iii) Given also that the equation X^2 +4x +c = 0 has unequal real roots, find the range of possible values of c.

    The answer is c < 4, but I have no idea how that was arrived at
    Discriminant must be positive?
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    b^2-4ac>0

    16x^2-4cx^2>0

    divide by 4x^2

    c < 4
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    (Original post by M14B)
    Discriminant must be positive?
    Good point.

    It is an edexcel question and C1 is a long way from complex numbers.
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    (Original post by SalazarSlytherin)
    b^2-4ac>0

    16x^2-4cx^2>0

    divide by 4x^2

    c < 4
    Gotcha!

    Many thanks Salazar
 
 
 
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