I am stuck on a quadratic equation question!!!

[peggyS]

[h=1]Q - Given that 3x^2+bx+10=a(x+3)^2+c Find the values of A,B,C[/h]I understand the basic principles of answering this question, for example, complete the square of this: 3x^2+bx+10 then use this to substitute and get the answers but i am really struggling with this particular question.

I would greatly appreciate any help because this is playing on my mind alot!!

*if possible can you please show me the steps you took to get the answer <3*

 

[Deleted member 4993]

Q - Given that 3x^2+bx+10=a(x+3)^2+c Find the values of A,B,C

I understand the basic principles of answering this question, for example, complete the square of this: 3x^2+bx+10 then use this to substitute and get the answers but i am really struggling with this particular question.

I would greatly appreciate any help because this is playing on my mind alot!!

*if possible can you please show me the steps you took to get the answer <3*

I do not understand this question:

You have used a, b and c in the expression (small letters) - and you are asking the values of A, B and C (capital letters).

Please re-read your post and correct it and re-post.

 

[Ishuda]

Q - Given that 3x^2+bx+10=a(x+3)^2+c Find the values of A,B,C

I understand the basic principles of answering this question, for example, complete the square of this: 3x^2+bx+10 then use this to substitute and get the answers but i am really struggling with this particular question.

I would greatly appreciate any help because this is playing on my mind alot!!

*if possible can you please show me the steps you took to get the answer <3*

Example:
17 x³ + 25 (x+2)² - b = a x³ +c x² + 100 x + 400
First do the multiple term expressions in parenthesis, i.e.
25 (x+2)² = 25 (x² + 4x + 4) = x² + 100 x + 100
So we have
17 x³ + x² + 100 x + 100 - b = a x³ +c x² + 100 x + 400
Now collect coefficients
(17-a) x³ + (1-c) x² + (100-100) x - ( b + 300) = 0
and continue

 

[Harry_the_cat]

Q - Given that 3x^2+bx+10=a(x+3)^2+c Find the values of A,B,C

I understand the basic principles of answering this question, for example, complete the square of this: 3x^2+bx+10 then use this to substitute and get the answers but i am really struggling with this particular question.

I would greatly appreciate any help because this is playing on my mind alot!!

*if possible can you please show me the steps you took to get the answer <3*

There are a few different ways you can do this question.

One way, as you said, is to complete the square. But an easier way would be:

Expand the RHS to get \(\displaystyle ax^2 + 6ax +9a +c\)

Now equate your coefficients from the LHS with the RHS:
3=a
b=6a
10=9a+c

and solve for a, b and c. I'll leave that up to you!
(Check your answer by substituting into the original equation and checking that both sides are the same.)

 

[peggyS]

Thanks everybody for your help!!!!

The answers which i got was A=3 B=18 and C=-17

could you please check these for me!!! <3

 

[stapel]

Thanks everybody for your help!!!!

The answers which i got was A=3 B=18 and C=-17

could you please check these for me!!! <3

What did you get when you checked, using the instructions provided to you in the previous reply?