Question

One factor of f (x ) = 4 x cubed minus 4 x squared minus 16 x + 16 is (x – 2). What are all the roots of the function? Use the Remainder Theorem.

Answer 1

Answer: B

Explanation:

Edge 2023

Answer 2

`f(x) =4 x {}^(3) - 4x {}^(2) - 16x + 16`

`divide \: by \: x - 2`

`4x {}^(2) \: into \: (x - 2) = 4x {}^(3) - 8x {}^(2)`

`g(x) = 4x {}^(2) - 16x + 16`

`4x \: into \: (x - 2) = 4x {}^(2) - 8x`

`z(x) = - 8x + 16`

`- 8 \: into \: (x - 2) = - 8x + 16 \\ no \: remainder`

`f(x) = (x - 2)(4x {}^(2) + 4x - 8)`

`f(x) = 0 \\ x - 2 = 0 \: \: \: \: \: \: \: \: \: 4x {}^(2) + 4x - 8 = 0 \\`

`x = \frac{ - 4 + \sqrt{4 {}^(2) - 4(4)( - 8) } }{2(4)} = ( - 4 + √(144) )/(8) = ( - 4 + 12)/(8) = 1`

`x = 2`

`x = ( - 4 - 12)/(8) = ( - 16)/(8) = - 2`