Question

A polynomial of the form $a{x}^5+b{x}^3+c{x}^2+dx+e$ has almost ________ zeroes.

• A. 3
• B. 5
• C. 7
• D. 11

Answer 1

The correct option is B 5

A polynomial of degree $n$ can have a maximum of $n$ zeroes because it can be expresssed as a product of atmost $n$ linear factors in $x$.

For example,$x^n+a_1{x}^{n-1}+...+a_n$ can be expressed as $(x-x_1)(x-x_2)....(x-x_n)$.

Here the polynomial ois of degree $5$.

Therefore, It can have a maximum of $5$ zeroes.