Solving for Values

[JSmith]

The polynomial function f(x) = ax⁴ - 3x³ - 63x² + 152x - b has one of its zeros at x = 5 and passes through the point (-2, -560).
Use the given information to determine the values of a and b.

So first, I thought I could solve for b using the zero at (5,0).

Therefore the equation would be f(x) = ax⁴ - 3x³ - 63x² + 152x + 5. However, when I plug -560=a(-2)⁴ - 3(-2)³ - 63(-2(² + 152(-2) + 5 in and solve, I end up with -33=16a. I really doubt this is the a value, so what am I doing wrong here?

 

[Deleted member 4993]

The polynomial function f(x) = ax⁴ - 3x³ - 63x² + 152x - b has one of its zeros at x = 5 and passes through the point (-2, -560).
Use the given information to determine the values of a and b.

So first, I thought I could solve for b using the zero at (5,0).

Incorrect


It should be:

0 = a*5⁴ -3*5³ - 63*5² + 152*5 - b

and it passes through (-2, -560). So:

-560 = a*(-2)⁴ -3*(-2)³ - 63*(-2)² + 152*(-2) - b

Two equations - two unknowns - solve.......

Therefore the equation would be f(x) = ax⁴ - 3x³ - 63x² + 152x + 5. However, when I plug -560=a(-2)⁴ - 3(-2)³ - 63(-2(² + 152(-2) + 5 in and solve, I end up with -33=16a. I really doubt this is the a value, so what am I doing wrong here?

.

 

[JSmith]

What am I doing wrong here?

 

[HallsofIvy]

What am I doing wrong here?

When solving for b, above, what happened to the "-63(5)^2= -1575"?