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Issue with finding the value of p in a quadratic (strange mark scheme?)

So I'm having some trouble with this question:


part a) I eventually got right, but for part b) I tried to factorise the equation and get the set of values p = 1 and p = 5. Then I drew the graph to find out that p > 5 and p < 1.

According to the mark scheme though, that is not the right answer. For some reason they don't want me to factorise the equation and instead solve it by completing the square.

My question is - how am I supposed to know that from the way they've asked it? Is my solution invalid for some reason?
Reply 1
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B_9710
18
Your answer is fine. In fact it's always better to factorise if the quadratic does in my opinion. As long as you got the right answers and used a valid method (which you did) then you get full marks.
Original post by frostyy
So I'm having some trouble with this question:


part a) I eventually got right, but for part b) I tried to factorise the equation and get the set of values p = 1 and p = 5. Then I drew the graph to find out that p > 5 and p < 1.


:holmes: 1 and 5 are not roots of that quadratic.
Reply 3
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frostyy
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17


This is the mark scheme. I might just not be reading it properly I guess?
Reply 4
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frostyy
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Original post by ghostwalker
:holmes: 1 and 5 are not roots of that quadratic.


I don't understand?
Reply 5
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B_9710
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In fact the quadratic does not factorise so you would have to complete the square.
Original post by frostyy
I don't understand?


Your quadratic does not factorise nicely, in particular it does not factorise to (p-1)(p-5). Multiply it out, as a check.

Hence the need to either use the quadratic formula or complete the square.
Reply 7
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frostyy
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Oh, okay. Sorry, I'm clearly a dumbass.

I have another question, if anyone could answer I'd be grateful.

When I have 12 / 2x it would equal 6 / x, which in turn is 6x^-1.

But why can't I do 12 / 2x = 12(2x^-1) to give 24x^-1 ? Then the answer would be 24 / x, which is incorrect. But why?
Original post by frostyy
Oh, okay. Sorry, I'm clearly a dumbass.

I have another question, if anyone could answer I'd be grateful.

When I have 12 / 2x it would equal 6 / x, which in turn is 6x^-1.

But why can't I do 12 / 2x = 12(2x^-1) to give 24x^-1 ? Then the answer would be 24 / x, which is incorrect. But why?


The 2x is in the denominator so it would become:

12/2x=12(2x)−112 / 2x = 12(2x)^{-1}

Which we can split if we desire, to:

=12(2)−1(x)−1 = 12(2)^{-1}(x)^{-1}

=6(x)−1 = 6(x)^{-1}
Reply 9
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frostyy
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Original post by ghostwalker
The 2x is in the denominator so it would become:

12/2x=12(2x)−112 / 2x = 12(2x)^{-1}

Which we can split if we desire, to:

=12(2)−1(x)−1 = 12(2)^{-1}(x)^{-1}

=6(x)−1 = 6(x)^{-1}


ok, thank you. What about this?: How is this correct?:


I did the calculation and the -1 + 1.5 + 6 = 6.5, not 3.5.

Where did they get the 3.5 from?
Original post by frostyy
So I'm having some trouble with this question:


part a) I eventually got right, but for part b) I tried to factorise the equation and get the set of values p = 1 and p = 5. Then I drew the graph to find out that p > 5 and p < 1.

According to the mark scheme though, that is not the right answer. For some reason they don't want me to factorise the equation and instead solve it by completing the square.

My question is - how am I supposed to know that from the way they've asked it? Is my solution invalid for some reason?


There's an easy way to find out if something factorises. If the discriminant from D=(b2)−4ac D = (b^2) - 4ac is equal to a square number, then the quadratic will factorise :smile:, otherwise just solve by either completing the square or using the quadratic formula.
Original post by frostyy
ok, thank you. What about this?: How is this correct?:


I did the calculation and the -1 + 1.5 + 6 = 6.5, not 3.5.

Where did they get the 3.5 from?


There's a minus sign before that 3/2.

I suggest taking a short break.
Reply 12
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frostyy
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Original post by ghostwalker
There's a minus sign before that 3/2.

I suggest taking a short break.


That may be a good idea.

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