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C1 question

Given that p is a constant such that 0 < p < 1, show that the equation

px^2 + 2x + (1-p) = 0

has two distinct roots


b^2 - 4ac > 0

2^2 - 4*p*(1-p) > 0

4 - (-4p^2 + 4p) > 0

4 + 4p^2 - 4p > 0

however 4p^2 - 4p + 4 doesn't have any real roots, where did I go wrong?
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solC
14
Original post by tammio
Given that p is a constant such that 0 < p < 1, show that the equation

px^2 + 2x + (1-p) = 0

has two distinct roots


b^2 - 4ac > 0

2^2 - 4*p*(1-p) > 0

4 - (-4p^2 + 4p) > 0

4 + 4p^2 - 4p > 0

however 4p^2 - 4p + 4 doesn't have any real roots, where did I go wrong?


Try completing the square with the discriminant
You haven't, the max value of P is 0.999.. and the smallest value is 0.0000....1, both of which when plugged into your equation result in your resulting inequality being solved hence there are 2 distinct roots, even if they are disgusting numbers.
Original post by tammio
Given that p is a constant such that 0 < p < 1, show that the equation

px^2 + 2x + (1-p) = 0

has two distinct roots


b^2 - 4ac > 0

2^2 - 4*p*(1-p) > 0

4 - (-4p^2 + 4p) > 0

4 + 4p^2 - 4p > 0

however 4p^2 - 4p + 4 doesn't have any real roots, where did I go wrong?
do either of you do economics In really stuck on a question?
Original post by Foodatastic
You haven't, the max value of P is 0.999.. and the smallest value is 0.0000....1, both of which when plugged into your equation result in your resulting inequality being solved hence there are 2 distinct roots, even if they are disgusting numbers.


I should be more clear. Your inequality states that p^2 - p + 1 > 0, any value for P will result in a positive number hence the quadratic is solvable.
I do economics, I can help hopefully
Original post by Fairy5eva
do either of you do economics In really stuck on a question?
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Avatar for tammio
tammio
OP
2
Original post by Foodatastic
You haven't, the max value of P is 0.999.. and the smallest value is 0.0000....1, both of which when plugged into your equation result in your resulting inequality being solved hence there are 2 distinct roots, even if they are disgusting numbers.


Thanks very much
IMG_0098.jpg
Original post by Foodatastic
I do economics, I can help hopefully


Do you know how to do b and c?
Original post by Fairy5eva
IMG_0098.jpg

Do you know how to do b and c?


Not too sure, I suspect we do different exam boards but I think for part B, the answer is £100bn as the real value should be the same as the nominal as the base rate is the first year, so inflation has no effect. GDP per head is the GDP per person, £100bn / population = GDP per capita (per head/person)
Original post by Foodatastic
Not too sure, I suspect we do different exam boards but I think for part B, the answer is £100bn as the real value should be the same as the nominal as the base rate is the first year, so inflation has no effect. GDP per head is the GDP per person, £100bn / population = GDP per capita (per head/person)

Thank you, im on edexcel by the way, do you agree with these answers:IMG_0100.PNG
Original post by Fairy5eva
Thank you, im on edexcel by the way, do you agree with these answers:IMG_0100.PNG


The method seems correct but I'm not too sure with your calculations on B, I think it may be the new year divided by base year, however I'm not too sure. Economics not my strong point haha. I'm doing OCR so I won't be of much use.
Original post by Foodatastic
The method seems correct but I'm not too sure with your calculations on B, I think it may be the new year divided by base year, however I'm not too sure. Economics not my strong point haha. I'm doing OCR so I won't be of much use.


Ahah okay, thanks anyway

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