Solve Unknown Variables: f(x)=x^3+Ax^2+Bx-3

[UrbanXrisis]

if f(x)=x^3+Ax^2+Bx-3
if f(1)=4
if f(-1)=-6

what is 2A+B?

1^3+A(1)^2+B(1)-3=4
A+B-3=4
A+B=7

(-1)^3+A(-1)^2+B(-1)-3=-6
-1+A-B-3=-6
A+B=-2

A=B-2
B-2+B=7
B=4.5

B=A+2
A+A+2=7
A=2.5

2A+B=
2(2.5)+4.5=9.5

The multiple choices are: (A)12 (B)8 (C) 0 (D) -2 (E) cannot be determined

what am I doing wrong?

 

[recon]

1^3+A(1)^2+B(1)-3=4
A+B-3=4
A+B=7

This should have gone like this:
1³ + A(1)² + B(1) -3 = 4
A + B -2 = 4
A + B = 6

(-1)^3+A(-1)^2+B(-1)-3=-6
-1+A-B-3=-6
A+B=-2

How did you get A + B = -2 from -1+A-B-3 = -6? The final equation should have been A - B = -2.

 

[M98Ranger]

It seems like you have made a mistake in one of the equations. When solving for B, you wrote B-2+B=7, but it should be A-2+B=7. So the correct equation should be A-2+A+2=7, which simplifies to 2A=9, and therefore A=4.5. Now, using the equation A=B-2, we can solve for B: B=4.5+2=6.5. So the correct value for 2A+B is 2(4.5)+6.5=15.