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Q:16If I and 3 are the zeros of the p(x) = 2x'- 7x - 13x + 63x -45, then find the remainingzeros of p(x). |
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Answer» zero of p(x) is 5 is the p(x)of thos question Since 1 and 3 are the zeros or roots of the given polynomial2x4- 7x3- 13x2+ 63x - 45, use the synthetic division method and factorize2x4- 7x3- 13x2+ 63x - 45 by dividing it with (x- 1) to get the remainder polynomial as 2x3- 5x2- 18x + 45.Now again divide the polynomial2x3- 5x2- 18x + 45 by (x - 3) to get the remainder as 2x2+ x - 15.Since the constant term in the equation2x2+ x - 15 is 15, it will be divisible by±3 ,±5, or± 15Use synthetic division again on the equation2x2+ x - 15 and factorize it by -3 to get the remainder as 2x - 5.Now, 2x - 5 has the root as 5/2.So, the zeros of2x4- 7x3- 13x2+ 63x - 45 are 1, 3,-3,5/2 |
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