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If p(x) = x3 – 6×2 + 11x – 1 then find p(1), p(2), p(3). Find p(x) – p(1), p(x) – p(2), p(x) – p(3), p(x) – p(1). Write the solutions of p(x) – p(1) = 0 |
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Answer» p(x) = x3 – 6x2 + 11x – 1 p(1) = 1 – 6 + 11 – 1 = 5 p(2) = 8 – 24 + 22 – 1 = 5 p(3) = 27 – 54 + 33 – 1 = 5 p(x) – p(1) = x3 – 6x2 + 11x – 6 p(x) – p(2) = x3 – 6x2 + 11x – 6 p(x) – p(3) = x3 – 6x2 + 11x – 6 p(x) – p(1) = x3 – 6x2 + 11x – 6 = 0 If x = 1, 2, 3 then p(x) – p(1) = 0. Factors of the equations are (x – 1), (x – 2), (x – 3). Solutions of the equations are 1, 2, 3. |
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