已知4x2-3x+1=a(x-1)2+b(x-1)+c对任意数x成立,则4a+2b+c=_.
问题描述:
已知4x2-3x+1=a(x-1)2+b(x-1)+c对任意数x成立,则4a+2b+c=______.
答
∵a(x-1)2+b(x-1)+c
=a(x2-2x+1)+bx-b+c
=ax2-2ax+a+bx-b+c
=ax2-(2a-b)x+a-b+c
=4x2-3x+1
∴a=4、-(2a-b)=-3、a-b+c=1,
解得:a=4、b=5、c=2,
∴4a+2b+c
=4×4+2×5+2
=16+10+2
=28
故答案为:28.