if 2^x -3x +1 = a(x-1)^2 + b(x-1)+c
find the values of a, b and c

Question

if 2^x -3x +1 = a(x-1)^2 + b(x-1)+c
 find the values of a, b and c

chaise · Answer

Are you sure it is supposed to be 2^x?

anonymous · Answer

oopss my apologies, its meant to be 2x^2

anonymous · Answer

Expand right side of the equation, then equate coefficients of both expressions. You ok with this?

anonymous · Answer

@ stroodle, would you be kind enough to show me the working out?

chaise · Answer

If:
2x^2-3x+1=a(x-1)^2 + b(x-1)+c
Make both equations equal to 0, when you do that they will be both equal to eachother.

2x^2-3x+1=0
a(x-1)^2+b(x-1)+c=0

Now you can solve the first equation.
x = 1 or x=1/2

Now you can substitute your x into that equation.. I'm not sure what to do from here.. but hopefully this helps. I might be wrong though.

anonymous · Answer

brb. I'll post another solution in 10-15mins if no-one else does.

chaise · Answer

You have four unknowns, you will need to somehow create for individual equations from that equation and solve them simultaneously. Possibly.

anonymous · Answer

umm thanks chaise. lets wait and see how stroodle does it!
stroodle your input is highly anticipated!

anonymous · Answer

if you expand rearrange the right side of the equation you should get:
$$ax^2+(b-2a)x+a+c-b$$
So now you can equate the coefficients of the two sides of the equation. i.e.
a=2 
b-2a=-3
a+c-b=1

anonymous · Answer

Let me know if you don't get it.

anonymous · Answer

why  thank you @ stroodle
i fully understand, thank you math whiz!