How many zeros does the polynomial $p (x) = 5$ have?

Class 9PolynomialsPolynomials

Step-by-Step Solution

p (x) = 5

gives the value 5 for every

x

, so it is never 0 — a non-zero constant polynomial has no zero at all. (Only the zero polynomial

p (x) = 0

is zero for every value of

x .

)

Answer: C) None

**Linear**: ax +

b = 0

→

x = - b / a

. One zero.

Example:

3 x - 12 = 0

→

x = 4

.

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

Example:

x^{2} - 5 x + 6 = 0

. Factor:

(x - 2) (x - 3) = 0

→

x = 2

x = 3

. Two zeros.

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

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