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C1 - Having trouble with a quadratic inequality question

Hello, I'm having trouble with the following edexcel question:

Find, as surds, the roots of the equation 2(x+1)(x-4)-(x-2)^2 = 0

So to begin with you know it won't factorise, so you need to complete the square or stick it into the formula.

2(x^2-3x-4)-x^2-4x+4 = 0
2x^2 - 6x - 8 - x^2 - 4x + 4 = 0
x^2 - 10x - 4 = 0

I put it into the formula and get (10 +- sqrt(116))/2

The answer should be 1 +- sqrt (13)

I have no idea where I have gone wrong, I just tried to complete the square and got 5 +- sqrt(29)

I'm so confused
Reply 1
Avatar for Andy98
Andy98
20
Original post by iron_lloyd
Hello, I'm having trouble with the following edexcel question:

Find, as surds, the roots of the equation 2(x+1)(x-4)-(x-2)^2 = 0

So to begin with you know it won't factorise, so you need to complete the square or stick it into the formula.

2(x^2-3x-4)-(x^2-4x+4) = 0
2x^2 - 6x - 8 - x^2 + 4x - 4 = 0


I put it into the formula and get (10 +- sqrt(116))/2

The answer should be 1 +- sqrt (13)

I have no idea where I have gone wrong, I just tried to complete the square and got 5 +- sqrt(29)

I'm so confused


Try again from there.
Reply 2
Avatar for gomc
gomc
11
2x2-6x-8-x2+4x-4=0
x2-2x-12=0

(x-1)2-12-1=0
(x-1)2-13=0
x-1=(sqr+-)13
x=1(sqr+-)13
Reply 3
Avatar for Andy98
Andy98
20
Original post by gomc
2x2-6x-8-x2+4x-4=0
x2-2x-12=0

(x-1)2-12-1=0
(x-1)2-13=0
x-1=(sqr+-)13
x=1(sqr+-)13


There we go. It was just one silly mistake you'd made :tongue:

EDIT: Also, this isn't an inequality
Reply 4
Avatar for iron_lloyd
iron_lloyd
OP
1
Original post by Andy98
Try again from there.


Oh dear.

x^2 - 2x - 12 = 0

(x-1)^2 - 13 = 0 therefore x = 1+- sqrt(13)

Thanks ever so much... I really must keep an eye out for that - before a squared bracket.

Edit: Yeah this part of the question isn't xD the next part is an inequality though, I just read off the question ^^
Reply 5
Avatar for iron_lloyd
iron_lloyd
OP
1
Original post by Andy98
There we go. It was just one silly mistake you'd made :tongue:

EDIT: Also, this isn't an inequality


I hope you don't mind me asking another question but I have a feeling the answer is wrong in their answer sheet.

You have to work out an area in the second part of a question to give you the equation:

x(x-5)<104

Which I got and was correct.

It then asks you to calculate the values of x given the previous answer:

x^2 - 5x - 104 < 0

putting that into the formula equation I get (5+- sqrt 446)/2 which gives me x = 13 or x = -8

In the answers x = 13 is correct however x = -8 is not, it should work out to be x=10.5


If I managed to get x=13 correct off the same quadratic formula I don't see why I get the second part wrong ?

Edit: I'm being really naive.. of course they haven't got the answers wrong!
(edited 8 years ago)
Reply 6
Avatar for Andy98
Andy98
20
Original post by iron_lloyd
Oh dear.

x^2 - 2x - 12 = 0

(x-1)^2 - 13 = 0 therefore x = 1+- sqrt(13)

Thanks ever so much... I really must keep an eye out for that - before a squared bracket.

Edit: Yeah this part of the question isn't xD the next part is an inequality though, I just read off the question ^^


Fair enough

Original post by iron_lloyd
I hope you don't mind me asking another question but I have a feeling the answer is wrong in their answer sheet.

You have to work out an area in the second part of a question to give you the equation:

x(x-5)<104

Which I got and was correct.

It then asks you to calculate the values of x given the previous answer:

x^2 - 5x - 104 < 0

putting that into the formula equation I get (5+- sqrt 446)/2 which gives me x = 13 or x = -8

In the answers x = 13 is correct however x = -8 is not, it should work out to be x=10.5


If I managed to get x=13 correct off the same quadratic formula I don't see why I get the second part wrong ?

Edit: I'm being really naive.. of course they haven't got the answers wrong!


You're not being naive - I got 5±4412\frac{5\pm\sqrt{441}}{2}, which comes out as x=13x=13 or x=−8x=-8

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