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Polynomials Test - 39

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Polynomials Test - 39
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  • Question 1
    1 / -0
    Which of the following represents a linear polynomial?
    Solution
    The general form of linear polynomial is $$p(x)=ax+b$$ where $$x$$ is a variable and $$b$$ is a constant. The first term of this polynomial has power $$1$$ and therefore, the degree of the polynomial is $$1$$.

    Similarly the polynomial $$p(x)=3x+4$$ has degree $$1$$.

    Hence, the polynomial $$p(x)=3x+4$$ is a linear polynomial.
  • Question 2
    1 / -0
    Which of the following is a linear polynomial?
    Solution
    $$\textbf{Step1: Check Every Option to find whether it is Linear Polynomial or Not}$$
                   $$\text{The General form of linear polynomial is p(x)=ax+b}$$    $$\text{[where x is a variable and b is a constant]}$$ 
                   $$\text{The first term of this polynomial has power 1 and Therefore, the degree of the polynomial is 1.}$$
                   $$\text{By Verifying every option,we can say that-}$$
                   $$\text{Only polynomial given in option D- p(x)=58+65+43+x=x+166 is in the form ax+b with degree 1}$$ 

     $$\textbf{Hence, the polynomial p(x)=58+65+43+x is a linear polynomial.}$$
  • Question 3
    1 / -0
    Which of the following is a linear polynomial?
    Solution
    $$\textbf{Step1: Check Every Option to Find Linear Polynomial}$$
                   $$\text{The General form of Linear Polynomial is p(x)=ax+b}$$
                   $$\text{where x is a Variable and b is a Constant}$$ 
                   $$\text{The first term of this polynomial has power 1 and Therefore, the degree of the polynomial is 1.}$$
                   $$\text{Since Linear Polynomial is Polynomial in terms Single variable with degree 1}$$ 
                   $$\text{ By Verifying every option,we can say that-}$$
                   $$\text{Option A.}$$  $$p(x)=6x^0=6(1)=6$$ $$\text{which is a Constant term}$$
                   $$\text{Option B.}$$   $$p(x)=4x^0=4(1)=4$$ $$\text{which is a Constant term}$$
                   $$\text{Option C.}$$  $$p(x)=2x^0=2(1)=2$$ $$\text{which is a Constant term}$$
                   $$\text{Option D.}$$  $$p(x)=\frac { 2x^{ 2 } }{ x }=2x$$ $$\text{which is a Linear Polynomial with Degree 1}$$ 
                   $$\text{$\therefore$ Only Polynomial given in option D- p(x)=2x is in the form ax+b with degree 1}$$ 

    $$\textbf{Hence, the Polynomial p(x)=2x is a Linear Polynomial.}$$

  • Question 4
    1 / -0
    Which of the following is NOT a constant polynomial?
    Solution
    We know that if the power of any variable is zero then the answer is always $$1$$. For example, $$x^0=1$$ which is a constant.

    Since $$p(x)=yx$$ is a polynomial with variables $$x,y$$ and there is no constant term in it.
     
    Hence, $$p(x)=yx$$ is not a constant polynomial.
  • Question 5
    1 / -0
    Which of the following represents a linear polynomial?
    Solution
    $$\Rightarrow$$ The general form of linear polynomial is $$p(x)=ax+b$$ where $$x$$ is a variable and $$b$$ is a constant. The first term of this polynomial has power $$1$$ and therefore, the degree of the polynomial is $$1$$.

    $$\Rightarrow$$ Similarly the polynomial $$p(x)=3x^1$$ or $$p(x)=3x$$ has degree $$1$$. where as in other optons the degree of $$p(x)$$ is not equal to $$1$$

    $$\Rightarrow$$ Hence, the polynomial $$p(x)=3x^1$$ is a linear polynomial.



  • Question 6
    1 / -0
    Which of the following is a linear polynomial?
    Solution
    $$\textbf{Step1: Check Every Option to find Linear Polynomial}$$
                   $$\text{The General form of linear polynomial is p(x)=ax+b}$$
                   $$\text{where x is a Variable and b is a Constant}$$ 
                   $$\text{The first term of this polynomial has power 1 and Therefore, the degree of the polynomial is 1.}$$
                   $$\text{Since Linear Polynomial is Polynomial in terms Single variable with degree 1}$$ 
                   $$\text{ By Verifying every option,we can say that-}$$
                   $$\text{$\therefore$ Only Polynomial given in option D- p(x)=x is in the form ax+b with degree 1}$$ 

    $$\textbf{Hence, the Polynomial p(x)=x is a Linear Polynomial.}$$

  • Question 7
    1 / -0
    Which of the following is a quadratic polynomial?
    Solution
    $$\textbf{Step-1: Apply the concept of polynomial.}$$
                     $$\text{The general form of quadratic polynomial is}$$  $$p(x)=ax^2+bx+c$$ $$\text{where}$$ $$x$$ 
                     $$\text{is a variable and}$$ $$a,b,c$$ $$\text{are constants.}$$ $$\text{The first term of this polynomial has power}$$ $$2$$ 
                     $$\text{and the second term of this polynomial has power 1 }$$                     
                     $$\text{and therefore, the degree of the polynomial is the largest exponent that is}$$ $$2$$.

                     $$\text{Similarly, the polynomial}$$ $$p(x)=5x^2+10$$ $$\text{has degree}$$ $$2$$.

                     $$\text{So, the polynomial}$$ $$p(x)=5x^2+10$$ $$\text{is a quadratic polynomial.}$$
    $$\textbf{Hence, correct option is D}$$
  • Question 8
    1 / -0
    Which of the following is NOT a quadratic polynomial?
    Solution
    $$\textbf{Step-1: Apply the concept of polynomial.}$$
                     $$\text{The general form of quadratic polynomial is}$$ $$p(x)=ax^2+bx+c$$ $$\text{where}$$ $$x$$ 
                     $$\text{is a variable and}$$ $$a,b,c$$ $$\text{are constants. The first term of this polynomial has power}$$ $$2$$ 
                     $$\text{and the second ter of this polynimial has power 1}$$ 
                     $$\text{and therefore, the degree of the polynomial is the largest exponent that is}$$ $$2$$.

                     $$\text{Therefore, a polynomial of degree two is called a quadratic polynomial.}$$

    $$\textbf{Hence, none of the options is a quadratic polynomial, option D}$$
  • Question 9
    1 / -0
    Which of the following is a quadratic polynomial?
    Solution
    $$\textbf{Step-1 Apply the concept of polynomial.}$$
                    $$\text{The general form of quadratic polynomial is}$$ $$p(x)=ax^2+bx+c ,$$ $$\text{where}$$ $$x$$ 
                    $$\text{is a variable and}$$ $$a,b,c$$ $$\text{are constants}$$ $$(a\ne 0).$$ $$\text{The first term of this polynomial has power}$$ $$2$$         
                    $$\text{and the second term of this polynomial has power 1}$$ 
                    $$\text{and therefore, the degree of the polynomial is the largest exponent that is}$$ $$2$$.

                    $$\text{Similarly, the polynomial}$$ $$p(y)=y^2+4$$$$\text{ has degree }$$$$2$$.

                    $$\text{So, the polynomial}$$ $$p(y)=y^2+4$$ $$\text{is a quadratic polynomial.}$$
    $$\textbf{Hence, correct option is B.}$$
  • Question 10
    1 / -0
    A polynomial of degree two is called _________.
    Solution
    The general form of quadratic polynomial is $$p(x)=ax^2+bx+c$$ where $$x$$ is a variable and $$a,b,c$$ are constants. '

    Hence, a polynomial of degree two is called a quadratic polynomial.
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