Math Help - function

1. function

Given the equation function $f(x)=4x^3-kx^2+x+3$, find the value of $k$ such that $(2x+1)$ is a factor

2. Originally Posted by william
Given the equation function $f(x)=4x^3-kx^2+x+3$, find the value of $k$ such that $(2x+1)$ is a factor
If $2x + 1$ is a factor, then by the factor and remainder theorems...

$f\left(-\frac{1}{2}\right) = 0$.

So we get

$4\left(-\frac{1}{2}\right)^3 - k\left(-\frac{1}{2}\right)^2 - \frac{1}{2} + 3 = 0$

$-\frac{1}{2} - \frac{1}{4}k + \frac{5}{2} = 0$

$2 = \frac{1}{4}k$

$8 = k$.