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Find the constants p, q and r...

Given that 2x^2 - 12x + p = q (x-r)^2 + 10 for all values of x, find the constants p, q and r.

If anyone knew how to do this, that would be really helpful for my C1 revision. : )

Reply 1

Larry<3

Rainbow-Dream

Given that 2x^2 - 12x + p = q (x-r)^2 + 10 for all values of x, find the constants p, q and r.

If anyone knew how to do this, that would be really helpful for my C1 revision. : )

Well firstly divide everything by two.

Now can you complete the square of x^2 - 6x + p/2?

Then just simply equate co-efficients. :smile:

Reply 2

Crazy Paving

As above although when dividing 'everything' by two, I think only the left hand side should be divided by two.

Reply 3

Rainbow-Dream

Larry<3

Well firstly divide everything by two.

Now can you complete the square of x^2 - 6x + p/2?

Then just simply equate co-efficients. :smile:

thanks, but how do you divide the right hand side by 2? and how do you equate co-efficients? sorry for all the questions. :s-smilie:

Reply 4

punkyrocker

Crazy Paving

As above although when dividing 'everything' by two, I think only the left hand side should be divided by two.

That's not really how maths works, surely?

Reply 5

ColinOfEdinburgh

Try multiplying (x-r)^2 out first and group the same order terms.
Take a look at the coefficients.

Reply 6

Crazy Paving

punkyrocker

That's not really how maths works, surely?

I should have made myself clearer.

I don't mean divide by two and completely get rid of it. I mean just factor the 2 out (so that it will end up still being there outside the brackets).

Reply 7

Crazy Paving

Rainbow-Dream

thanks, but how do you divide the right hand side by 2? and how do you equate co-efficients? sorry for all the questions. :s-smilie:

Dont actually divide both sides by two. Just factor two out of the left hand side to make completing the square easier.

To equate the coefficients once you have completed the square on the left hand side, hopefully they will be in the same form. Then just look at which number is in the letters positon on the other side and there are your answers.

Reply 8

Andylol

Simply complete the square on the left hand side and the rest should be clear!

Reply 9

punkyrocker

Crazy Paving

I should have made myself clearer.

I don't mean divide by two and completely get rid of it. I mean just factor the 2 out (so that it will end up still being there outside the brackets).

Sorry, I didn't meant to be arsey, I just misunderstood :h:

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