Question

Write a polynomial equation with integer coefficients that has the given roots.

Answer 1

ANSWER:

$x^{3}+5x^{2}+4x$

STEP-BY-STEP EXPLANATION:

If we have the roots, which would be the zeros of an equation, then we convert each root into a factor and the product of all these factors is the polynomial, like this:

$\begin{gathered} x=0 \\ \\ x-4\rightarrow x+4=0 \\ \\ x-1\operatorname{\rightarrow}x+1=0 \\ \end{gathered}$

We multiply them like this:

$\begin{gathered} x\cdot \left(x+4\right)\left(x+1\right) \\ \\ x\cdot(x^2+x+4x+4) \\ \\ x^3+x^2+4x^2+4x \\ \\ x^3+5x^2+4x \end{gathered}$

Therefore, the polynomial equation that has the given roots is:

$x^{3}+5x^{2}+4x$