Question

given that √3 is a zero of the polynomial x cube - x square - 3X-Men 3. find the other zeros​

Answer 1

Answer:

The other zeros are $1\:and\:-\sqrt3$

Step-by-step explanation:

Given polynomial is

$x^3-x^2-3x+3$

since $\sqrt3$ is a zero, the given

polynomial can be written as

$x^3-x^2-3x+3=(x-\sqrt3)(x^2+px-\sqrt3)$

Equating coefficients of x on both sides

$-3=-\sqrt{3}p-\sqrt3$

$-3+\sqrt3=-\sqrt{3}p$

$3-\sqrt3=\sqrt{3}p$

$p=\sqrt{3}-1$

The other quadratic factor is

$x^2+(\sqrt{3}-1)x-\sqrt{3}$

$=x(x+\sqrt{3})-x-\sqrt{3}$

$=x(x+\sqrt{3})-1(x+\sqrt{3})$

$=(x-1)(x+\sqrt{3})$

$\therefore$ The other zeros are

$1\:and\:-\sqrt3$