InterviewSolution
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InterviewSolution
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If P(x) is a polynomial with integer coefficients such that for 4 distinct integers `a, b, c, d,P(a) = P(b) = P(c) = P(d) = 3`, if `P(e) = 5`, (e is an integer) thenA. e = 1B. e = 3C. e = 4D. no real value of e |
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Answer» Correct Answer - 4 `P(a) = P(b) = P(c) = P(d) = 3` `rArr P(x) = 3` has a, b, c, d as its roots `rArr P(x) - 3 = (x - a)(x - b)(x - c)(x - d) Q(x)` [`because Q(x)` has integral coefficient] Given P(e) = 5, then `(e - a) (e - b) (e - c) (e - d) Q(e) = 5` This is possible only when at least three of the five integers (e-a),(e-b),(e-c),(e-d), Q(e) re equal to 1 or -1. Hence, two of them will be equal, which is not possible. Since a, b, c, d are distinct integers, P(e) = 5 is not possible. |
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