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Obtain all other zeros of a polynomial 2 x ki power 4 + 3 x cube minus 15 x square - 24 x minus 8 if two of its zeros are 2 root 2 and minus 2 root 2 |
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Answer» Answer: Step-by-step explanation: Solve the equation x3 − 3x2 – 2x + 4 = 0 We put the numbers that are factors of 4 into the equation to see if any of them are correct. f(1) = 13 − 3×12 – 2×1 + 4 = 0 1 is a SOLUTION f(−1) = (−1)3 − 3×(−1)2 – 2×(−1) + 4 = 2 f(2) = 23 − 3×22 – 2×2 + 4 = −4 f(−2) = (−2)3 − 3×(−2)2 – 2×(−2) + 4 = −12 f(4) = 43 − 3×42 – 2×4 + 4 = 12 f(−4) = (−4)3 − 3×(−4)2 – 2×(−4) + 4 = −100 The only integer solution is x = 1. When we have found one solution we don’t really NEED to test any other numbers because we can now solve the equation by dividing by (x − 1) and trying to solve the quadratic we get from the DIVISION. |
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