A mystery k? Make it a slider
Find a missing coefficient by sliding k, then read the other roots straight off the graph.
1:34 · Nonlinear Functions
Worked in this video
p(x) = 2x³ + kx² − 11x + 6, where k is a constant, has x = ½ as one of its roots.
What is the value of k?
On paper this means plugging ½ into every term, with a cube and a square of a fraction, and solving for k — easy to drop a factor of 2. In Desmos, type p(x) with the k left in and add a slider for k. A root at ½ means p(½) = 0, so type p(½) on the next line and drag k until that value reads 0. It does at k = −3, and the curve now passes through (½, 0).
Answer: k = −3