Questions & Answers

Let f(x) be a polynomial such that \[f\left( \dfrac{-1}{2} \right)=0\] , then a factor of f(x) is
A. 2x-1
B. 2x+1
C. x-1
D. x+1

Answer Verified Verified
Hint: For a polynomial, there could be some values of the variable for which the polynomial will be zero. These values are called zeros of a polynomial. Sometimes, they are also referred to as roots of the polynomials. In general, we use them to find the zeros of quadratic equations, to get the solutions for the given equation.

Complete step-by-step answer:
Knowing the above mentioned definition of zeros of a polynomial, we can easily find the answer of the given question.
As mentioned in the question, we have to find the factor of f(x) using the information that is given in the question.
Now, we know that on putting \[x=\left( \dfrac{-1}{2} \right)\], the function becomes zero that is \[f\left( \dfrac{-1}{2} \right)=0\] which means \[x=\left( \dfrac{-1}{2} \right)\] is a zero of the polynomial f(x), hence, we can write as follows
\[\left( x+\dfrac{1}{2} \right)\] is a factor of f(x) which can also be represented as follows
(2x+1) is the factor of f(x), so, option (b) is the correct answer.

Note: The students can make an error if they don’t know about the definitions and the meaning of zeros of a polynomial or zeros of a function as without knowing the definition of zeros of a function; one can never get to the correct answer.