P(x) be a polynomial of at most degree 5 which leaves remainders -1 and 1 upon division by (x-1)3 and (x+1)3 respectively.
1) Number of real roots of P(x) = 0
(a) 1 (b) 3 (c) 5 (d) 2
2) The maximum value of y=P''(x) can be obtained at x =
(a) -1/√3 (b) 0 (c) 1/√3 (d) 1
3) The sum of pairwise prduct of all roots (real and complex) of P(x) = 0 is
(a) -5/3 (b) -10/3 (c) 2 (d) -5
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3 Answers
49put P(x)=(x-1)3.f(x) - 1
and P(x)=(x+1)3.g(x) + 1
f(x) and g(x) are polynomials of degree at most 2
i think that would solve the problem! :)
1arey yaar......i also had such an approach and cud solve the first two.... but not third....so posted this question.... plzz elaborate third one...