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Math question help!

I have a question that I'm trying to make sense of

In theory if (ax+b)^2 + (cx+d)^2 = 0

what would be x?

I know it can be zero but I don't know what number it could be as any negative number squared is positive square number, so I'm always going to end up with more than 0.

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Reply 1
Original post by bblondon
I have a question that I'm trying to make sense of

In theory if (ax+b)^2 + (cx+d)^2 = 0

what would be x?

I know it can be zero but I don't know what number it could be as any negative number squared is positive square number, so I'm always going to end up with more than 0.

As both squared terms are >=0, what must their value be for their sum to be 0.
Then what is x in terms of a and b and also in terms of c and d. Obviously unless there is a certain relationship between a, b, c and d, there may be no solution.
Reply 2
Original post by mqb2766
As both squared terms are >=0, what must their value be for their sum to be 0.
Then what is x in terms of a and b and also in terms of c and d. Obviously unless there is a certain relationship between a, b, c and d, there may be no solution.


Well I don't think there is a relationship between them unless I really become nitpicky but I was just concerned if saying "there's no solution" to this question is allowed- since the exact wording was solve this equation?
Reply 3
Original post by bblondon
Well I don't think there is a relationship between them unless I really become nitpicky but I was just concerned if saying "there's no solution" to this question is allowed- since the exact wording was solve this equation?


Can you post a picture of the full question along with your working?
Reply 4
Original post by mqb2766
Can you post a picture of the full question along with your working?

I can't show the exact question since it would be against the guide lines of my lecture / class but I can try and make up a similar question?

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

Even if the answer workouts to be a decimal or 0 or whatever, I don't mind. What I'm curious about is HOW to work it out, like the steps and process.
Reply 5
Original post by bblondon
I can't show the exact question since it would be against the guide lines of my lecture / class but I can try and make up a similar question?

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

Even if the answer workouts to be a decimal or 0 or whatever, I don't mind. What I'm curious about is HOW to work it out, like the steps and process.


Sounds weird not posting the question, and it could be that the original expression has the particular relationship between coefficients, but your modified one doesnt.

But if youre unsure about the expression on the left, why not plot in in desmos and see if it ever equals zero. Then follow the hints in #2 for thinking about the individual parts and post what you think.
Reply 6
Original post by mqb2766
Sounds weird not posting the question, and it could be that the original expression has the particular relationship between coefficients, but your modified one doesnt.

But if youre unsure about the expression on the left, why not plot in in desmos and see if it ever equals zero. Then follow the hints in #2 for thinking about the individual parts and post what you think.


Yeah, it sucks not really being able to post the question- it's cause the course I'm taking says we should'nt ask for help with the same question but we could use a variation of it and ask for help. But alas, since even I don't understand the question I guess my "variation" questions isn't really helpful 😂😂. The questions are meant to challenge us and if we can't answer it then it's fine but I just really wanted to see the working out of it yk?

Also I plotted it just now, safe to say desmos says nothing, so I'm guessing that this really has no solution so I'll leave it at that!

Thank you mqb2766, have a splendid day!
Original post by bblondon
I have a question that I'm trying to make sense of

In theory if (ax+b)^2 + (cx+d)^2 = 0

what would be x?

I know it can be zero but I don't know what number it could be as any negative number squared is positive square number, so I'm always going to end up with more than 0.


After what I got here, I think it is not the purpose to find an exact value for x, but a general term or terms for the parameters in.
Reply 8
Original post by bblondon
Yeah, it sucks not really being able to post the question- it's cause the course I'm taking says we should'nt ask for help with the same question but we could use a variation of it and ask for help. But alas, since even I don't understand the question I guess my "variation" questions isn't really helpful 😂😂. The questions are meant to challenge us and if we can't answer it then it's fine but I just really wanted to see the working out of it yk?

Also I plotted it just now, safe to say desmos says nothing, so I'm guessing that this really has no solution so I'll leave it at that!

Thank you mqb2766, have a splendid day!


Cant help thinking youre missing the point a bit. Its a bit like when you factorise a quadratic and argue that one of the linear factors must be zero in order to find the roots. Here you have the sum of two squared expressions, so they are both >= 0, so for their sum to be 0, their values must be ... and this means that x must be ... Its not that hard.

So you should be able to understand why your made up question has no solutions and hopefully get to understand what condition must exist if there is to be single solution.
(edited 8 months ago)
Reply 9
Original post by bblondon
I can't show the exact question since it would be against the guide lines of my lecture / class but I can try and make up a similar question?

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

Even if the answer workouts to be a decimal or 0 or whatever, I don't mind. What I'm curious about is HOW to work it out, like the steps and process.

How can one question cause an issue ... post it please or we can''t help properly.
Original post by bblondon
Yeah, it sucks not really being able to post the question- it's cause the course I'm taking says we should'nt ask for help with the same question but we could use a variation of it and ask for help. But alas, since even I don't understand the question I guess my "variation" questions isn't really helpful 😂😂. The questions are meant to challenge us and if we can't answer it then it's fine but I just really wanted to see the working out of it yk?

Also I plotted it just now, safe to say desmos says nothing, so I'm guessing that this really has no solution so I'll leave it at that!

Thank you mqb2766, have a splendid day!

Which course demands this or is this really a competition or assessment?
Reply 11
Original post by Muttley79
Which course demands this or is this really a competition or assessment?

It’s COMPOS
Original post by bblondon
It’s COMPOS


So you should have been honest in your original post ...
(edited 8 months ago)
Reply 13
Original post by mqb2766
Cant help thinking youre missing the point a bit. Its a bit like when you factorise a quadratic and argue that one of the linear factors must be zero in order to find the roots. Here you have the sum of two squared expressions, so they are both >= 0, so for their sum to be 0, their values must be ... and this means that x must be ... Its not that hard.

So you should be able to understand why your made up question has no solutions and hopefully get to understand what condition must exist if there is to be single solution.

The question was splint into pet A and Part B, with my first question here being Part B. I’m having a feeling that I did not understand part A correctly and therefore I can’t understand Part B. I’m assuming that if I change the letters (it was only just letters) it’ll be fine to post but now idk but here’s the question

a^2 + b^2 = 0

Here’s my thought process:

My assumptions were that a or a^2 cannot equal to 0 neither can b or b^2 If it could then obviously it would be 0 for both

My other assumption was that a cannot equal to b
Reply 14
Original post by Muttley79
So you should have been honest in your original post ...


Sorry! I thought “course” would’ve sufficed enough but I don’t understand what was dishonest about my post?
Original post by bblondon
Sorry! I thought “course” would’ve sufficed enough but I don’t understand what was dishonest about my post?


I menat the first post in this thread where you asked for help.
Reply 16
Original post by bblondon
The question was splint into pet A and Part B, with my first question here being Part B. I’m having a feeling that I did not understand part A correctly and therefore I can’t understand Part B. I’m assuming that if I change the letters (it was only just letters) it’ll be fine to post but now idk but here’s the question

a^2 + b^2 = 0

Here’s my thought process:

My assumptions were that a or a^2 cannot equal to 0 neither can b or b^2 If it could then obviously it would be 0 for both

My other assumption was that a cannot equal to b


THere may be more in the original question than youve posted, though for
f^2 + g^2 = 0
the only solution, fairly obviously, is f=g=0. If f and g are functions of x as per #1 or #5, then you get something like
https://www.desmos.com/calculator/wka01ezuh3
Note Ive changed the a,b,c,d coefficients to make the graph scale ok, but you can obviously play with them. Note that f(x) and g(x) are zero at a particular value of x, so what must happen for their sum to be zero at a single point ... Just play with it a bit and see if you can analyse what happens and why

It might help to also note that
(2x + 10)^2
and
(x+5)^2
are both zero at the same value of x (but obviously their curvature will be different). Also, fairly obviously, if you add two parabolas you get another parabola.
(edited 8 months ago)
Original post by bblondon
I can't show the exact question since it would be against the guide lines of my lecture / class but I can try and make up a similar question?

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

Even if the answer workouts to be a decimal or 0 or whatever, I don't mind. What I'm curious about is HOW to work it out, like the steps and process.


Okay, that is a concrete equation, that is different. My steps:

Spoiler




Just press on the spoiler button, if you tried everything by yourself. :wink:
(edited 8 months ago)
Original post by Kallisto
Okay, that is a concrete equation, that is different. My steps;

Sorry, but I don't think this is helpful here. The whole point of the question is to understand that if you have a problem:

f(x)2+g(x)2=0f(x)^2 + g(x)^2 = 0,

it is possible to reduce this to two independent (and relatively easy) problems, one only involving f(x), one only involving g(x).

Multiplying out and summing will work, but it's not the intended approach. (It's possible to just look at this and see what the solutions are (if any)).

[As a surprisingly close analogy: if someone asked "how do I find the roots of (x2)(x3)=0(x-2)(x-3) = 0?" then multiplying out and using the quadratic formula will work, but you're obviously supposed to do it by solving (x-2) = 0 and (x-3) = 0.]
Original post by DFranklin
Sorry, but I don't think this is helpful here. The whole point of the question is to understand that if you have a problem:

f(x)2+g(x)2=0f(x)^2 + g(x)^2 = 0,

it is possible to reduce this to two independent (and relatively easy) problems, one only involving f(x), one only involving g(x).

(...)


Okay, I am curious know and you have awaken my interest. Tell me how it is possible to reduce this two independent problems to make it easier? what are your thoughts?

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