Question

Find a cubic polynomial whose zeroes are 2, −3 and 4

Answer 1

If the zeroes of the cubic polynomial are a, b and c then the cubic polynomial can be found as
$x^3-\left(a+b+c\right)x^2+\left(ab+bc+ca\right)x-abc$ ...(1)
Let $a=2,b=-3\mathrm{and}c=4$
Substituting the values in (1), we get
$$\begin{gathered} x^3-\left(2-3+4\right)x^2+\left(-6-12+8\right)x-\left(-24\right) \\ \Rightarrow x^3-3x^2-10x+24 \end{gathered}$$