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How to find a polynomial given its zeros

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A polynomial in x whose zeros are-2,-1 and 3 is 
  1. x^3+7x+6
  2. x^3+7x-6
  3. x^3+7x+6
  4. x^3-7x-6

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    first of all if you are in exam hall, you can quickly know that the answer must be either option 2 or option 4. This is because when you multiply all the constants after changing their signs from ( -2, -1, and 3) to (2, 1, -3) you will have -6. Let’s solve in details… = (x +2)(x + 1)(x -3), multiplying the first two brackets, we have: = (x^2 + x + 2x + 2)(x – 3) = (x^2 + 3x + 2)(x – 3), and completing the multiplication, we have: = x^3 + 3x^2 + 2x – 3x^2 – 9x – 6. = x^3 + 2x – 9x – 6 = x^3 – 7x – 6 (option 4 is correct!)

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