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A polynomial p of degree 5 has exactly 3 distinct real zeroes, and its graph just touches (does not cross) the -axis at one of them.
What is the smallest total number of real zeroes counted with multiplicity that this graph can show?

Class 10Zeroes of a PolynomialAlgebra — Polynomials
  • A4
  • B3
  • C5
  • D8

Step-by-Step Solution

Two zeroes are simple crossings (count 1 each = 2). One zero is a touch, so it is repeated at least twice (count 2). Minimum total counted with multiplicity = 1 + 1 + 2 = 4 (the 5th would come from further multiplicity or complex zeroes).
Answer: A) 4

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