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Let $p (x) = a x^{2} + bx + c$ be a quadratic polynomial. It can have at most

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Two zeroes

One zero

Three zeroes

None of these

answer is B.

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Detailed Solution

Given, polynomial

p (x) = a x^{2} + bx + c .

The polynomial

a x^{2} + bx + c

has three terms.
The first one is

a x^{2}

, the second is

bx

, and the third is c.
The degree of the polynomial

a x^{2} + bx + c

is the highest exponent which is 2.
Since,

a x^{2} + bx + c

is a quadratic polynomial, it can have zero, one or two zeroes.
Thus, the polynomial

a x^{2} + bx + c

can have at most two zeroes.
Hence, the correct option is 2.

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