GATE | GATE-CS-2000 | Question 49
A polynomial p(x) satisfies the following:
p(1) = p(3) = p(5) = 1
p(2) = p(4) = -1
The minimum degree of such a polynomial is
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (D)
Explanation:
p(1) = p(3) = p(5) = 1
p(2) = p(4) = -1
The polynomial touches 0 at least once from 1 to 2, so there
is a root between 1 to 2
The polynomial touches 0 at least once from 2 to 3, so there
is a root between 2 to 3
Similarly, there is at least one root from 3 to 4 and 4 to 5.
So minimum degree is 4.
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Last Updated :
28 Jun, 2021
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