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Calculate all the roots of equation x^4 - (5/2)x^3 - (1/2)x^2 - (5/2)x - (3/2) = 0

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juniorsilvamath | Student, Undergraduate | Honors

Posted March 15, 2013 at 5:33 PM via web

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Calculate all the roots of equation x^4 - (5/2)x^3 - (1/2)x^2 - (5/2)x - (3/2) = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 15, 2013 at 8:10 PM (Answer #3)

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The equation x^4 - (5/2)x^3 - (1/2)x^2 - (5/2)x - (3/2) = 0 has to be solved.

x^4 - (5/2)x^3 - (1/2)x^2 - (5/2)x - (3/2) = 0

=> 2x^4 - 5x^3 - x^2 - 5x - 3 = 0

=> 2x^4 - 6x^3 + x^3 - 3x^2 + 2x^2 - 6x + x - 3 = 0

=> 2x^3(x - 3) + x^2(x - 3) + 2x(x - 3) + 1(x - 3) = 0

=> (x - 3)(2x^3 + x^2 + 2x + 1) = 0

=> (x - 3)(x^2(2x + 1) + 1(2x + 1)) = 0

=> (x - 3)(x^2 + 1)(2x + 1) = 0

(x - 3) = 0

=> x = 3

(2x + 1) = 0

=> x = -1/2

(x^2 + 1) = 0

=> x^2 = -1

=> x = -i and x = i

The roots of the equation are {-i, i, -1/2, 3}

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