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how to solve this equation in the real number system:

2x^(3) + 3x^(2) + 2x + 3 = 0

steps please

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1 answer
  1. 2X^3 + 3X^2 + 2X + 3 = 0.

    First, we reduce the cubic Eq to a guadratic Eq by finding a value of x that satisfies the Eq. This was done by
    trial and error. However, the task was made a lot easier by the use of EXCEL Spread sheets.

    It was determined x = -1.5 satisfies the cubic Eq:

    x = -1.5 = -1 1/2 = -3/2.

    x = -3/2,
    x + 3/2 = 0,
    Multiply both sides by 2 and get:
    2x + 3 = 0.
    Using long division, we divide the cubic Eq by 2x + 3:

    (2x^3 + 3x^2 +2x + 3)/(2x + 3)=
    x^2 + 1.
    Now we can easily solve the quad. Eq:

    x^2 + 1 = 0,

    x2 = -1,
    x = sqrt(-1) = +- i.

    Solution set: x = - 3/2, x = i, x = -i.

    So there are 3 solutions which is the max. for a cubic Eq.

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