Question

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

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

Answer 1

Answer: (B)

Two zeros

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 exponent of the first term is $2$.

The exponent of the second term is $1$ because $bx=b{x}^1$.

The exponent of the third term is $0$ because $c=c{x}^0$.

Since the highest exponent is $2$, therefore, the degree of $a{x}^2+bx+c$ is $2$.

Since, the degree of the polynomial is $2$, hence, the polynomial $a{x}^2+bx+c$ can have zero, one or two zeroes.

Hence, the polynomial $a{x}^2+bx+c$ can have at most two zereos.