What are the roots of the polynomial equation x4+x3=4x2+4x? Use a graphing calculator and a system of equations. A.)–2, –1, 0, 2 B.)–2, 0, 1, 2 C.)–1, 0 D.)0, 1

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QUESTION POSTED AT 18/04/2020 - 07:30 PM

Answered by admin AT 18/04/2020 - 07:30 PM

x^4+x^3=4x^2+4x\\\\x^4+x^3-4x^2-4x=0\\\\x\Big[x^3+x^2-4x-4\Big]=0\\\\
x\Big[x^2\big(x+1\big)-4\big(x+1\big)\Big]=0\\\\x\Big[\big(x+1\big)\big(x^2-4\big)\Big]=0\\\\x\big(x+1\big)\big(x^2-4\big)=0\\\\
x\big(x+1\big)\big(x+2\big)\big(x-2\big)=0\\\\\\x=0\quad\vee\quad x+1=0\quad\vee\quad x+2=0\quad\vee\quad x-2=0\\\\
\boxed{x=0\quad\vee\quad x=-1\quad\vee\quad x=-2\quad\vee\quad x=2}

Answer A.
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