what are the roots of the polynomial equation $x^{4}+x^{2}=4x^{3}-12x + 12$? use a graphing calculator and a…

what are the roots of the polynomial equation $x^{4}+x^{2}=4x^{3}-12x + 12$? use a graphing calculator and a system of equations. round noninteger roots to the nearest hundredth.\n-12, 20\n-2.73, 2, 2.73\n-1.73, 1.73, 2\n-20, 12

what are the roots of the polynomial equation $x^{4}+x^{2}=4x^{3}-12x + 12$? use a graphing calculator and a system of equations. round noninteger roots to the nearest hundredth.\n-12, 20\n-2.73, 2, 2.73\n-1.73, 1.73, 2\n-20, 12

Answer

Explanation:

Step1: Rewrite the equation

Rewrite $x^{4}+x^{2}=4x^{3}-12x + 12$ as $x^{4}-4x^{3}+x^{2}+12x - 12=0$.

Step2: Use a graphing - calculator

Graph the function $y = x^{4}-4x^{3}+x^{2}+12x - 12$. The $x$ - intercepts of the graph are the roots of the polynomial equation. When we graph the function $y=x^{4}-4x^{3}+x^{2}+12x - 12$ using a graphing calculator, we find that the roots of the equation are approximately $x=-1.73,1.73,2$.

Answer:

C. $-1.73,1.73,2$