Thread: Find coefficients

My problem is:

If 3x^2 - 2x + 1 = a(x-1)^2 + b(x-1) + c , find the value of a^2 + b^2 - c^2.

The answer is 21; how would you get that? Thanks.

Originally Posted by Averee

My problem is:

If 3x^2 - 2x + 1 = a(x-1)^2 + b(x-1) + c , find the value of a^2 + b^2 - c^2.

The answer is 21; how would you get that? Thanks.

a(x-1)^2+b(x-1)+c

a(x^2-2x+1)+b(x-1)+c

ax^2-2ax+a+bx-b+c

ax^2+(-2a+b)x+(a+c)

Thus,
a=3 and -2a+b=-2 and a+c=1

Find a,b,c
Then you can find your answer.

Thank you.