what are the roots of the polynomial equation x^3-7xx=6x-12? use a graphing calculator and a system of equations. A. -6, 6B. -4, 1, 3C. -3, -1, 4D. 1, 3​

Answer:The roots of the polynomial equation x^3 - 7x = 6x - 12 is 1, 3, -4 Hence option B is correctSolution:Given that the polynomial equation is [tex]x^{3}-7 x=6 x-12[/tex]We are asked to find the roots of the polynomial[tex]x^{3}-7 x=6 x-12[/tex][tex]x^{3}-7 x-6 x+12=0[/tex]On solving we get,[tex]x^{3}-13 x+12=0[/tex][tex]x^{3}-12 x-x+12=0[/tex][tex]\begin{array}{l}{x\left(x^{2}-1\right)-12(x-1)=0} \\\\ {x\left(x^{2}-1\right)-12(x-1)=0}\end{array}[/tex](x-1)(x(x+1)-12)=0 (x-1)(x-3)(x+4)=0 x = 1, 3, -4  Hence the roots of the polynomial equation x^3 - 7x = 6x - 12 is 1, 3, -4 Hence option B is correct