Question

Say true or false. A polynomial cannot have more than one zero.
A. True
B. False

Answer 1

Hint: Zeros of any equation mean the number of solutions of that equation.
Polynomial equation is an expression composed of variables, exponents and constants equating equal to zero.

Complete step by step answer:
The expressions formed with variables, exponents and constants equating equal to zero. We can find the zeros of a polynomial equation by factorization (i.e., by factoring them in terms of degree and variables present in the equation.
General representation of the polynomial equation is: ${{a}_{0}}{{X}^{n}}+{{a}_{1}}{{X}^{n-1}}+{{a}_{2}}{{X}^{n-2}}+{{a}_{3}}{{X}^{n-3}}+......+{{a}_{n-1}}{{X}^{1}}+{{a}_{n}}{{X}^{0}}$( where a$_{0},{{a}_{1}},{{a}_{2}},{{a}_{3}},{{a}_{3}}...$are constant with ${{a}_{0}}\ne 0$ multiplied with variables term.)
Total number of zeros of an equation is equal to the highest power of the variable in that polynomial equation.
As we change the value of n (exponents of the variables) we can further categorize the polynomial equation into:
n=$1$ the equation becomes ${{a}_{0}}X+{{a}_{1}}$ which is an equation in one variable, therefore it is also known as a monomial equation. We can the value of X by equating it with zero i.e., ${{a}_{0}}X+{{a}_{1}}$=0. For example: $2X+3=0$ we get the value of x=$-\dfrac{3}{2}$.(only possible zero of the equation).
n=$2$the equation becomes ${{a}_{0}}{{X}^{2}}+{{a}_{1}}X+{{a}_{2}}$which has only two variable terms and highest degree is two, such type of equation is known as binomial equation. Zeros of such type of equation can be calculated by factorization and we get a total of $2$zeros.
n=$3$ the equation becomes \[{{a}_{0}}{{X}^{3}}+{{a}_{1}}{{X}^{2}}+{{a}_{2}}{{X}^{1}}+{{a}_{3}}\]and therefore we get total of $3$zeros.
From the above result we come to the conclusion that yes, a polynomial can have one or more zero.

So, the correct answer is “Option B”.

Note: Total number of zeros of a polynomial equation is equal to the highest power of the variable present in the equation.