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1. Find constants a, b an c such that, for all values of x.

3x^2-5x+1 = a(x+b)^2+c
2. (Original post by leigh.xoxo)
Find constants a, b an c such that, for all values of x.

3x^2-5x+1 = a(x+b)^2+c
what have you done so far?
3. (Original post by TenOfThem)
what have you done so far?
don't think this is right but all i've done so far is
x(3x+5)^2-25+1
4. (Original post by leigh.xoxo)
don't think this is right but all i've done so far is
x(3x+5)^2-2+1
Do you know how to complete the square

OR

Have you been taught how to compare coefficients
5. (Original post by TenOfThem)
Do you know how to complete the square

OR

Have you been taught how to compare coefficients
We were taught how to complete the square, but not been shown how to do it with a number in front of the x.
6. (Original post by leigh.xoxo)
We were taught how to complete the square, but not been shown how to do it with a number in front of the x.

Can you complete the square on the expression in the bracket?
7. (Original post by TenOfThem)
Do you know how to complete the square

OR

Have you been taught how to compare coefficients
yeah im clueless but gave it ago
x(x-5/6)^2- 25/36 + 1/3
8. (Original post by TenOfThem)
Do you know how to complete the square

OR

Have you been taught how to compare coefficients
How could you do this by comparing coefficients?
I've heard of this when someone talks of the factor theorem. What is it?
9. (Original post by leigh.xoxo)
yeah im clueless but gave it ago
x(x-5/6)^2- 25/36 + 1/3
you have an x outside the bracket instead of the 3

So you are getting there

Now, add the fractions and multiply by the 3
10. (Original post by MathMeister)
How could you do this by comparing coefficients?
I've heard of this when someone talks of the factor theorem. What is it?
expand the RHS and then put the coefficients for each element equal
11. (Original post by TenOfThem)
expand the RHS and then put the coefficients for each element equal
Thanks!
12. (Original post by TenOfThem)
you have an x outside the bracket instead of the 3

So you are getting there

Now, add the fractions and multiply by the 3
thanks its making sense now x
13. (Original post by leigh.xoxo)
thanks its making sense now x
ok

I am now going to show you equating the coefficients as you may find it even easier

expanding the right hand side

so

Looking at the term you can see that 3 = a

Looking at the term you can se that -5 = 2ab = 6b so you can find b

Then looking at the constant you can see 1 = ab2 + c so you can find c

This is just an alternative method - either works

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