SOLVING POLYNOMIAL EQUATIONS WITH DIFFERENT POWERS

(1)  Solve the following equations

(i) sin² x − 5sin x + 4 = 0         Solution

(ii) 12x³ + 8x = 29x² − 4     Solution

(2)  Examine for the rational roots of

(i) 2x³ − x² − 1 = 0     Solution

(ii) x⁸ − 3x + 1 = 0     Solution

(3)  Solve 8 x^3/2n - 8 x^-3/2n  =  63        Solution

(4)  Solve

Solution

(5)  Solve the equations

(i) 6x⁴ − 35x³ + 62x² − 35x + 6 = 0     Solution

(ii)  x⁴ + 3x³ - 3x - 1     Solution

(6)  Find all real numbers satisfying 4^x − 3(2^x+2 ) + 2⁵ = 0.

Solution

(7)  Solve the equation 6x⁴ − 5x³ − 38x² − 5x + 6 = 0 if it is known that 1/3 is a solution.       Solution

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