Use a graphing calculator and a system of equations to find the roots of the equation. x4 − 4x3 = 6x2 − 12x From least to greatest, what are the integral roots of the equation?answer is -2,0

Answer:The roots are -2 , 0 , (3 - √3) , (3 + √3)The integral roots are -2 , 0Step-by-step explanation:∵ x^4 - 4x³ = 6x² - 12x∴ x^4 - 4x³ - 6x² + 12x = 0∴ x(x³ - 4x² - 6x + 12) = 0∴ x = 0 ∴ x³ - 4x² - 6x + 12 = 0∵ f(-2) = (-2)³ - 4(-2)² - 6(-2) + 12 = -8 - 16 + 12 + 12 = 0∴ (x + 2) is a factor of the equation x³ - 4x² - 6x + 12 = 0∴ (x³ - 4x² - 6x + 12) ÷ (x + 2) = (x² - 6x + 6)(x + 2)∴ (x² - 6x + 6)(x + 2) = 0∴ x + 2 = 0 ⇒ ∴ x = -2∴ x² - 6x + 6 = 0 ⇒ quadratic equation (ax² + bx + c = 0)∵ a = 1 , b = -6 , c = 6∵ [tex]x=\frac{-b+\sqrt{b^{2}-4ac}}{2a}=\frac{6+\sqrt{36-24}}{2}=\frac{6+2\sqrt{3}}{2}=3+\sqrt{3}[/tex]∴ x = 3 + √3 and x = 3 - √3∴ The roots are -2 , 0 , (3 - √3) , (3 + √3)