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Polynomials Test - 44

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Polynomials Test - 44
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  • Question 1
    1 / -0
    The graph of a polynomial is shown in given figure, then the number of its zeroes is

    Solution
    Number of Zeroes are the value at which for any value of x,  y is zero

    Here at 3 points y becomes 0, so No. of zeros are 3
  • Question 2
    1 / -0
    Which of the following is a linear expression:
    Solution
    When an algebraic expression consist of only one variable whose power is $$1$$, it is known as linear expression.
    Thus, $$1+z$$ is the only expression in which single variable is given with power $$1$$.
  • Question 3
    1 / -0
    Which of the following equations has the sum of its roots as 3?
    Solution
    The correct answer is option $$(B)$$
    Main concept used: Sum of roots (a, $$\beta $$) of quadratic equation $$ax^{2} + bx + c = 0$$ is $$a+\beta = \dfrac{-b}{a} $$

    (a) Given equation is $$2x^{2} - 3x + 6 =0$$
    Here, $$a+\beta = \dfrac{3}{2} \neq 3$$
    So, the given equation has not the sum of roots as 3.

    (b) Given equation is - $$x^{2} + 3x - 3 = 0$$
    Here, $$a+\beta = \dfrac{-3}{-1} = 3$$
    $$\therefore $$ The given equation has sum of its roots as 3.

    (c) Given equation is
    $$\sqrt{2}x^{2} - \dfrac{3}{\sqrt{2}}x + 1 = 0$$
    Here, $$a + \beta = \dfrac{-\left ( \dfrac{-3}{\sqrt{2}} \right )}{\sqrt{2}}=\dfrac{+3}{\sqrt{2}\sqrt{2}}=\dfrac{3}{2}\neq 3$$
    So, the given equation has not the sum of roots as 3.

    (d) Given equation is $$3x^{2} -3x + 3 = 0$$
    Here, $$a + \beta = \dfrac{-(-3)}{3} = 1 \neq 3$$
    So, the given equation has not the sum of roots as 3.

  • Question 4
    1 / -0
    A quadratic polynomial, whose zeroes are $$-3$$ and $$4$$ is
    Solution
    Quadratic equation with $$\alpha$$ and $$\beta$$ as roots can be written as
    $$ x^2 - (\alpha + \beta) + \alpha\beta=0$$

    Here, $$\alpha = -3$$ and $$\beta = 4$$
    $$\therefore \alpha + \beta = -3 + 4 = 1$$
    and $$\alpha - \beta = -3 \times 4 = -12$$

    $$\therefore$$ The quadratic equation is
    $$x^2 - (\alpha + \beta)x + \alpha\beta=0$$
    $$\Rightarrow  x^2 - 1x - 12=0$$
    $$\Rightarrow  \dfrac{x^2}{2} - \dfrac{x}{2} - \dfrac{12}{2}=0$$
    $$\Rightarrow \dfrac{x^2}{2} - \dfrac{x}{2} - 6=0$$

    Hence the quadratic polynomial is $$ \dfrac{x^2}{2} - \dfrac{x}{2} - 6$$
  • Question 5
    1 / -0
    The degree of a quadratic polynomial is:
    Solution
    The highest power of the variable in a polynomial in one variable is called the degree of the polynomial.

    Quadratic polynomial is a polynomial in which highest order of the variable is $$2$$.

    For example, $$2x^2+5x+1=0$$ is a quadratic equation and it has a degree $$2$$.

    Thus, degree of quadratic polynomial is $$2$$.

    Therefore, option $$C$$ is correct.
  • Question 6
    1 / -0
    If $$f(x) = 8$$then$$ f(x)$$ is called
    Solution
    If $$f(x) = 8$$ then $$ f(x)$$ is called Constant polynomials
  • Question 7
    1 / -0
    The degree of polynomial is $$x + 2$$ is:
    Solution
    $$\textbf{Step 1: Apply the property of polynomial.}$$

                    $$\text{We have, x + 2}$$
                    $$\text{We know that the highest power of the variable in a polynomial in one variable is }$$
                    $$\text{called the degree of the polynomial.}$$
                    $$\text{Here, the highest power of variable x is 1.}$$

    $$\textbf{Thus, degree of polynomial is 1, option - (B).}$$
  • Question 8
    1 / -0
    Write the correct alternative answer for the following question:
    Which is the degree of the polynomial $$ 2x^{2} + 5x^{3} + 7 $$ ?
    Solution
    The given polynomial is $$ 2x^{2} + 5x^{3} + 7 $$.

    We know, in a polynomial in one variable, the highest power of the polynomial term with a non-zero coefficient, is called the degree of the polynomial.
    Here, the highest power of the variable $$x$$ is $$3$$.

    $$\therefore$$ The degree of the given polynomial is $$3$$.
    Therefore, option $$A$$ is correct.
  • Question 9
    1 / -0
    Write the correct answer for the following question 
    Which of the following is a linear polynomial?
    Solution

  • Question 10
    1 / -0
    The degree of the polynomial $$x^4 + x^3$$ is:
    Solution
    The highest power of the variable in a polynomial in one variable is called the degree of the polynomial.

    Here, in the given polynomial $$x^4 + x^3$$, the highest power of the variable $$x$$ is $$4$$.
    $$\therefore$$ The degree of the given polynomial is $$4$$.

    Therefore, option $$D$$ is correct.
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