Investigate the properties of the polynomial equation f(x) = x + 5x6 +x4 - x +...

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Investigate the properties of the polynomial equation f(x) = x² + 5x6 +x4 - x³ + x² - 2 = 0, by proceeding as follows. (a) By writing the fifth-degree polynomial appearing in the expression for f'(x) in the form 7x5 + 30x4 + a(x - b)² + c, show that there is in fact only one positive root of f(x) = 0. (b) By evaluating f(1), f(0) and f(-1), and by inspecting the form of f(x) for negative values of x, determine what you can about the positions of the real roots of f(x) = 0 Investigate the properties of the polynomial equation f(x) = x² + 5x6 +x4 - x³ + x² - 2 = 0, by proceeding as follows. (a) By writing the fifth-degree polynomial appearing in the expression for f'(x) in the form 7x5 + 30x4 + a(x - b)² + c, show that there is in fact only one positive root of f(x) = 0. (b) By evaluating f(1), f(0) and f(-1), and by inspecting the form of f(x) for negative values of x, determine what you can about the positions of the real roots of f(x) = 0

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