Answers

2016-07-19T21:02:45+08:00
You can factor the equation to get (x + 1)(x + 3)(x + 5) = 0. So the roots are -1, -3, and -5. a) If doubled, the roots become -2, -6, and -10. The equation is: (x + 2)(x + 6)(x + 10) = x^3 + 18x^2 + 92x + 120 b) Reversing signs gives the solutions to be 1, 3, and 5. Thus, the equation required is: (x - 1)(x - 3)(x - 5) = x^3 - 9x^2 + 23x - 15 c) Two less than the original equation's solutions' are -3, -5, and -7. An equation is: (x + 3)(x + 5)(x + 7) = x^3 + 15x^2 + 71x + 105 d) The solutions' reciprocals are -1, -1/3 and -1/5. Thus, an equation is: (x + 1)(x + 1/3)(x + 1/5) = (x + 1)(3x + 1)(5x + 1) = 15x^3 + 23x^2 + 9x + 1 I hope this helps!
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