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Algebra/Factorising Question (or at least I think it is :s) - HSN forum # Algebra/Factorising Question (or at least I think it is :s)

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Posted 15 March 2006 - 08:18 PM

Hey, can somebody complete & explain how this question is done? I'd be very greatful, cheers: (Area of the first rectangle is A1 and area of the second is A2)

A1 - A2 = x2 - (8p + 4)x - 8p

Given that A1-A2 = 1cm2, establish the value of p, where p>-1, for this equation to have only one solution for x.

And hence find x when p takes this value.

### #2dfx

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Posted 15 March 2006 - 10:15 PM This equation will only have one solution (of x) if the discriminant = 0 i.e. real and equal roots (effectively one root).

So solve for and get your value of p.

And then just plug it back in for the value of x and solve the original quadratic.

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Posted 16 March 2006 - 06:46 PM This equation will only have one solution (of x) if the discriminant = 0 i.e. real and equal roots (effectively one root).

So solve for and get your value of p.

And then just plug it back in for the value of x and solve the original quadratic. How did you manage to arrive at this? Edit: Bleh, not sure if I'm doing this right... Correct so far?

### #4Dave

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Posted 16 March 2006 - 07:31 PM

the line you dont understand comes about because there is a common factor of X in there. This makes sense as a quadratic is in the form Ax2+bx + c. noteing that p is just a number so -8p-1 is a constant

and b = -(8p+4)

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Posted 16 March 2006 - 08:06 PM

the line you dont understand comes about because there is a common factor of X in there. This makes sense as a quadratic is in the form Ax2+bx + c. noteing that p is just a number so -8p-1 is a constant

and b = -(8p+4)

Ah, yeah, silly me. I wrote it down correct when I was doing the calculation but typed it out wrong. Anyhoo, I got: p = -20/8 and p = -4 for some reason. Er, what did I do wrong this time?

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Posted 16 March 2006 - 09:18 PM

the line you dont understand comes about because there is a common factor of X in there. This makes sense as a quadratic is in the form Ax2+bx + c. noteing that p is just a number so -8p-1 is a constant

and b = -(8p+4)

Ah, yeah, silly me. I wrote it down correct when I was doing the calculation but typed it out wrong. Anyhoo, I got: p = -20/8 and p = -4 for some reason. Er, what did I do wrong this time?

I put *** where I think you went wrong - well this line is still correct but it the line following it is wrong. Keep the 64p^2 + 96p + 20 equal to zero, take out a common factor of four to get 4(16p^2 + 96p + 20) = 0. Now you have to split the part inside the bracket into two different brackets, and then find the values for p which make the brackets, and therefore the whole thing, equal to zero. One of them should be greater than -1.
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Posted 16 March 2006 - 11:51 PM

the line you dont understand comes about because there is a common factor of X in there. This makes sense as a quadratic is in the form Ax2+bx + c. noteing that p is just a number so -8p-1 is a constant

and b = -(8p+4)

Ah, yeah, silly me. I wrote it down correct when I was doing the calculation but typed it out wrong. Anyhoo, I got: p = -20/8 and p = -4 for some reason. Er, what did I do wrong this time?

I put *** where I think you went wrong - well this line is still correct but it the line following it is wrong. Keep the 64p^2 + 96p + 20 equal to zero, take out a common factor of four to get 4(16p^2 + 96p + 20) = 0. Now you have to split the part inside the bracket into two different brackets, and then find the values for p which make the brackets, and therefore the whole thing, equal to zero. One of them should be greater than -1.

I think you're right - I tried that and got an answer of -0.25, so erm, yea. Thanks everybody. ### #8John

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Posted 17 March 2006 - 01:14 PM

the line you dont understand comes about because there is a common factor of X in there. This makes sense as a quadratic is in the form Ax2+bx + c. noteing that p is just a number so -8p-1 is a constant

and b = -(8p+4)

Ah, yeah, silly me. I wrote it down correct when I was doing the calculation but typed it out wrong. Anyhoo, I got: p = -20/8 and p = -4 for some reason. Er, what did I do wrong this time?

I put *** where I think you went wrong - well this line is still correct but it the line following it is wrong. Keep the 64p^2 + 96p + 20 equal to zero, take out a common factor of four to get 4(16p^2 + 96p + 20) = 0. Now you have to split the part inside the bracket into two different brackets, and then find the values for p which make the brackets, and therefore the whole thing, equal to zero. One of them should be greater than -1.

But if you take out a factor of 4 you get 4(16p^2 + 24p + 5)
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Posted 18 March 2006 - 10:39 AM

the line you dont understand comes about because there is a common factor of X in there. This makes sense as a quadratic is in the form Ax2+bx + c. noteing that p is just a number so -8p-1 is a constant

and b = -(8p+4)

Ah, yeah, silly me. I wrote it down correct when I was doing the calculation but typed it out wrong. Anyhoo, I got: p = -20/8 and p = -4 for some reason. Er, what did I do wrong this time?

I put *** where I think you went wrong - well this line is still correct but it the line following it is wrong. Keep the 64p^2 + 96p + 20 equal to zero, take out a common factor of four to get 4(16p^2 + 96p + 20) = 0. Now you have to split the part inside the bracket into two different brackets, and then find the values for p which make the brackets, and therefore the whole thing, equal to zero. One of them should be greater than -1.

But if you take out a factor of 4 you get 4(16p^2 + 24p + 5) Oops, I can never put down what I mean when I'm typing maths. Thanks for pointing that out.

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