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Rohit claims that is a zero of . Which response is correct?

Class 9PolynomialsPolynomials
  • ANo — p(2) = 4, so 2 is not a zero.
  • BYes — p(2) = 0, so 2 is a zero.
  • CNo — p(2) = −4, so 2 is not a zero.
  • DYes — because 2 divides the constant term 4.

Step-by-Step Solution

p(2) = 8 − 12 + 8 − 4 = 0, so Rohit is right. The reason matters too: a number is a zero because substituting it makes the polynomial 0, not merely because it divides the constant term.
Answer: B) Yes — p(2) = 0, so 2 is a zero.

Key idea: Finding zeros (roots)

**Linear**: ax + → . One zero.

Example: → .

**Quadratic**: solve by factorisation, or quadratic formula (Class 10).

Example: . Factor: → or . Two zeros.

**General principle**: a polynomial of degree n has AT MOST n real zeros.

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