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Question

Let p(x)=ax2+bx+c be a quadratic polynomial. It can have at most

A
One zero
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B
Two zeros
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C
Three zeros
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D
None of these
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Solution

The correct option is D Two zeros
The polynomial ax2+bx+c has three terms. The first one is ax2, the second is bx, and the third is c.

The exponent of the first term is 2.

The exponent of the second term is 1 because bx=bx1.

The exponent of the third term is 0 because c=cx0.

Since the highest exponent is 2, therefore, the degree of ax2+bx+c is 2.

Since, the degree of the polynomial is 2, hence, the polynomial ax2+bx+c can have zero, one or two zeroes.

Hence, the polynomial ax2+bx+c can have at most two zereos.

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