Answer to Question #269847 in Algebra for pica

Question

Given that 2𝑥 − 5 is a factor of polynomial functions 𝑓(𝑥) = 𝑘𝑥^2 − 𝑏𝑥 + 3𝑘, determine the ratio k : b in the simplest form.

Answer 1

If $2𝑥 − 5$ is a factor of polynomial functions $𝑓(𝑥) = 𝑘𝑥^2 − 𝑏𝑥 + 3𝑘,$ then

$$𝑓(\dfrac{5}{2}) = 𝑘(\dfrac{5}{2})^2 − 𝑏(\dfrac{5}{2}) + 3𝑘=0$$

$$25k-10b+12k=0$$

$$37k=10b$$

$$k:b=10:37$$