Question

Write the coefficient of ${x}^{2}$ in each of the following:-
a)\[17\text{ }-\text{ }2x\text{ }+\text{ }7{{x}^{2}}\]
b)\[9\text{ }-\text{ }12x\text{ }+\text{ }{{x}^{3}}\]
c)\[\dfrac{\pi }{6}~{{x}^{2}}-\text{ }3x\text{ }+\text{ }4\]
d)\[\sqrt{3}x-\text{ }\text{ }7\]

Answer 1

Hint:-Before solving this question, let us first know about Polynomials, and Coefficient.
POLYNOMIALS: Polynomials are algebraic expressions that comprise of exponents which are added, subtracted or multiplied. Polynomials are of different types: namely Monomial, Binomial, and Trinomial. A monomial is a polynomial with one term. A binomial is a polynomial with two, unlike terms.
COEFFICIENTS: A number used to multiply a variable is called a coefficient.

Complete step-by-step answer:
For example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient.
Variables having no number have a coefficient of 1.
Example: x is really 1x.

Let us now solve this question.
We shall consider every option.
a)\[17\text{ }-\text{ }2x\text{ }+\text{ }7{{x}^{2}}\]
We can see that there are three terms in this expression. The term that contains ${x}^{2}$ is the third term, i.e. ‘ \[7{{x}^{2}}\] ’ .
So, here, in this term, the coefficient of ‘ \[{{x}^{2}}\] ’ is 7.

b)\[9\text{ }-\text{ }12x\text{ }+\text{ }{{x}^{3}}\]
We can see that there are three terms in this expression. But, none of these three terms contain ‘ \[{{x}^{2}}\] ’.
Therefore, the coefficient of ‘ \[{{x}^{2}}\] ’ is 0.

c)\[\dfrac{\pi }{6}~{{x}^{2}}-\text{ }3x\text{ }+\text{ }4\]
We can see that there are three terms in this expression. The term that contains ‘ \[{{x}^{2}}\] ’ is the first term, i.e. ‘ \[\dfrac{\pi }{6}~{{x}^{2}}\] ‘ .
So, here, in this term, the coefficient of ‘ \[{{x}^{2}}\] ’ is \[\dfrac{\pi }{6}\] .

d)\[\sqrt{3}x-\text{ }\text{ }7\]We can see that there are two terms in this expression. But, none of these two terms contain ‘ \[{{x}^{2}}\] ’.
Therefore, the coefficient of ‘ \[{{x}^{2}}\] ’ is 0.

Note:-Let us now learn about monomials, binomials, trinomials and terms.
MONOMIALS: A monomial is a polynomial with one term. For example: \[2xy,\text{ }3{{a}^{3}}\] , etc.
BINOMIALS: A binomial is a polynomial with two, unlike terms. For example: \[2xy\text{ }+\text{ }3{{x}^{2}},\text{ }3{{a}^{3}}-\text{ }5y\], etc.
TRINOMIALS: A trinomial is a polynomial with three terms, which are unlike. For example:
\[~2xy\text{ }+\text{ }3{{x}^{2}}+\text{ }4,\text{ }3{{a}^{3}}-\text{ }5y\text{ }+\text{ }8\] , etc.
TERMS: A term is either a single number or variable, or the product of several numbers or variables. Terms are separated by a + or - sign in an overall expression. For example: In the trinomial \[2xy\text{ }+\text{ }3{{x}^{2}}+\text{ }4;\text{ }2xy,\text{ }3{{x}^{2}}\] , and 4 are the three separate