Roots of cubic polynomial. To solve a cubic equation, the best strategy is to guess one of three roots.. Example 04: Solve the equation $ 2x^3 - 4x^2 - 3x + 6 = 0 $. Step 1: Guess one root. The good candidates for solutions are factors of the last coefficient in the equation.
Then you consider the polynomial $$ p(-x) = (-x)^5 + 2(-x)^3 + (-x)^2 + 2 = -x^5 - 2x^3 + x^2 + 2 $$ This polynomial only has one sign change in the coefficients so it can at most have one positive root meaning the original polynomial may at most have one real negative root .
The solution to the equation 5x + 6 = 2 (2x - 3) is x = -12. The given equation is: 5x + 6 = 2 (2x - 3) Expand the right hand side of the equation using distributive rule. 5x + 6 = 4x - 6. Collect like terms.
Step 1: Subtract 3 from both sides of the inequality. Step 3: Divide both sides of the inequality by the coefficient of x. 5 - 8x < 2x + 3? Add 8x to both sides of the inequality. What value of x is in the solution set of 3 (x - 4) ≥ 5x + 2? What value of x is in the solution set of 8x - 6 > 12 + 2x?
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For a. the answer is +5 and -5 since ( + 5) 2 = 25 and ( - 5) 2 = 25. For b. the answer is +5 since the radical sign represents the principal or positive square root. Whole numbers such as 16, 25, 36, and so on, whose square roots are integers, are called perfect square numbers .
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