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# C! Maths problem

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1. 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
2. (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?
3. b^2-4ac>0

16x^2-4cx^2>0

divide by 4x^2

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

It is an edexcel question and C1 is a long way from complex numbers.
5. (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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