Question

Given the following roots, choose the coefficients of the polynomial in standard form : 1 and 7

Answer 1

for the first root x=1

$\begin{gathered} x=1 \\ (x-1) \end{gathered}$

for the second root x=-7i

$\begin{gathered} x=-7i \\ x^2=-49 \\ (x^2+49) \end{gathered}$

to find the polynomial in standard form we multiply both expressions:

$(x-1)\cdot(x^2+49)$$x^3-x^2+49x-49$