Maths algebra help please !!!!!!

Original post by Snowystar

Hi. I was wondering if anybody could help me to understand this question, if you could that would help a lot many thanks!!

Work out the value of m, k and n:

2x^2+8x+k=m(x-n)^2+5n

The answers are
M=2 n=-2 k=-2

And I am completely confused!

Hiya

For this question it's best to look at the differences on both sides, on the left you have a standard quadratic, and on the right you have a quadratic (with the coefficients missing) written as you would when you are completing the square.

Does this make it any clearer?

Reply 3

RogerOxon

21

You have on quadratic in x equal to another. For them to be equal for all values of x, the coefficients of each of the terms (x^2, x and constant) must be equal. Expand the RHS and you will be able to calculate the values of the constants k, m and n.

To get started, the coefficient of x^2 on the LHS is 2. If you expand the RHS, its x^2 coefficient is m, so m=2. Do the same the the x and constant terms.

(edited 7 years ago)

Reply 4

OP

Original post by KaylaB

Hiya

For this question it's best to look at the differences on both sides, on the left you have a standard quadratic, and on the right you have a quadratic (with the coefficients missing) written as you would when you are completing the square.

Does this make it any clearer?

Yes I see now! Thank you!

Reply 5

Original post by Snowystar

Yes I see now! Thank you!

No problem, if you have any further issues with it just give me a shout

Reply 6

the bear

carefully remove the brackets on the RHS & compare the various powers of x on both sides.

Reply 7

OP

Original post by Snowystar

Yes I see now! Thank you!

Wait I still don't understand how to get k though

Reply 8

Original post by Snowystar

Wait I still don't understand how to get k though

So if you now know the values of m and n (m = 2 and n = -2)
You can find k by recognising that -8 + k = 5n
And since you know the value of n you can just substitute that value in and find k

Reply 9

OP

Original post by KaylaB

So if you now know the values of m and n (m = 2 and n = -2)
You can find k by recognising that -8 + k = 5n
And since you know the value of n you can just substitute that value in and find k

Ok got it is the following question right?

X^2-6x+k=m(x-n)^2+2n
Does m=1 n=3 and k=-6
?

(edited 7 years ago)

Reply 10

Original post by Snowystar

Ok got it is the following question right?

X^2-6x+k=m(x-n)^2+2n
Does m=1 n=3 and k=-6
?

Not quite, do you mind posting your working so I can help guide you through it?

Reply 11

OP

Original post by KaylaB

Not quite, do you mind posting your working so I can help guide you through it?

No i don't mind. I really appreciate the help, thank you 😊

X^2-6x+k=m(x-n)^2+2n
So straight away m=1

Then i deal with the left of the equation to get (x-3)^2 +k or (x-3)^2 +9
So n must be 3
So now the right hand side
(X-3)^2 +9+(2x3)
To get back to 9 do -6 so k is -6

There's my working i actually have no idea why i done the things that I done but ...

Reply 12

RogerOxon

21

Original post by Snowystar

So now the right hand side
(X-3)^2 +9+(2x3)
To get back to 9 do -6 so k is -6

There's my working i actually have no idea why i done the things that I done but ...

Where did the +9 come from?

I find it easier to multiply-out the RHS, rather than completing the square on the LHS.

Reply 13