Question

If f(x) = 4x^3 + Ax^2 + 7x - 1 and f(2) = 3, what is the value of A?
(^ = powers)

Answer 1

A = -10.5

Explanation:

To find the value of "A", you can plug x = 2 and f(x) = 3 into the equation. This will allow you to simplify and find the value of "A".

f(x) = 4x³ + Ax² + 7x - 1 <---- Original equation

3 = 4(2)³ + A(2)² + 7(2) - 1 <---- Plug x = 2 and f(x) = 3 into equation

3 = 4(8) + A(4) + 14 - 1 <---- Solve 2³ and 2²

3 = 32 + A(4) + 14 - 1 <---- Multiply 4 and 8

3 = 45 + A(4) <---- Combine like terms

-42 = A(4) <---- Subtract 45 from both sides

-10.5 = A <---- Divide by 4

If A = -10.5, the final equation would look like this:

f(x) = 4x³ - 10.5x² + 7x - 1

Answer 2

A = -10.5

Explanation:

If f(2) = 3, then...

For that certain input, 2 = x. It also gives us an output of 3, meaning that...

`3 = 4x^3 + Ax^2 + 7x - 1`

Since we know that 2 = x, we can substitute 2 for x in the equation...
`3=4(2^3) + A(2^2) + 7(2) - 1`

Simplify the right side:

`3=4(8) + A(4) + 7(2) - 1\\3=32+4A+14-1\\3=32+4A+13\\3=45+4A\\`

Subtract 45 from both sides:

`3-45=45-45+4A`

`-42=4A`

Divide both sides by 4:

`(-42)/(4)=(4A)/(4)\\-10.5=A`

CHECK:

`f(x)=4x^3-10.5x^2+7x-1\\f(2)=4(2^3)-10.5(2^2)+7(2)-1\\f(2)=4(8)-10.5(4)+14-1\\f(2)=32-42+14-1\\f(2)=-10+14-1\\f(2)=4-1\\f(2)=3 \rightarrow \text{Correct!}`

Therefore,

A = -10.5