What are the roots of the polynomial equation x to the 4th power plus x squared is equal to 4 x cubed minus 12 x plus 12 ? Use a graphing calculator and a system of equations. Round noninteger roots to the nearest hundredth.

Set the two sides equal and move everything to one side: x⁴ − 4x³ + x² + 12x − 12 = 0. Factoring gives (x − 2)²(x² − 3) = 0, so the roots are x = 2 and x = ±√3. Since √3 ≈ 1.73, the roots are −1.73, 1.73, and 2, matching choice A.

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