Question

Write the polynomial given the roots:x = 0 and 5 and sqrt 3

Answer 1

The given roots are,

$x=0,\text{ 5, }\sqrt[]{3}$

To write the polynomial equation:

The polynomial equation can be formed by writing the roots like as follows,

$\begin{gathered} x(x-5)(x-\sqrt[]{3})=(x^2_{}-5x)(x-\sqrt[]{3}) \\ =x^3-5x^2-\sqrt[]{3}x^2+5\sqrt[]{3}x \\ =x^3-(5+\sqrt[]{3})x^2+5\sqrt[]{3}x \end{gathered}$

Hence, the polynomial equation is,

$x^3-(5+\sqrt[]{3})x^2+5\sqrt[]{3}x$