SOLUTION: Solve the equation 28 x cubed plus 88 x squared minus 37 x minus 7 equals 0 given that negative seven halves is a zero of f left parenthesis x right parenthesis equals 28 x cubed

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Question 1208854: Solve the equation 28 x cubed plus 88 x squared minus 37 x minus 7 equals 0 given that negative seven halves
is a zero of f left parenthesis x right parenthesis equals 28 x cubed plus 88 x squared minus 37 x minus 7.
Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


You are given a cubic equation and one of its roots. Use synthetic division (or long division) to reduce the cubic equation to a quadratic equation; then use factoring or the quadratic formula to find the two remaining roots.

  -3.5  |  28   88  -37   -7
        |
        +--------------------
           28

  -3.5  |  28   88  -37   -7
        |      -98
        +--------------------
           28  -10

  -3.5  |  28   88  -37   -7
        |      -98   35
        +--------------------
           28  -10   -2

  -3.5  |  28   88  -37   -7
        |      -98   35    7
        +--------------------
           28  -10   -2    0

The remaining quadratic polynomial is 28x%5E2-10x-2. For finding the other two roots, we can remove the common factor of 2 to get 14x%5E2-5x-1

This factors to give us two rational roots:

14x%5E2-5x-1=%287x%2B1%29%282x-1%29

The two remaining roots are -1/7 and +1/2.

ANSWER: The three roots, all rational, are -7/2, -1/7, and 1/2.