SolveItNCERT · CBSE Boards

NCERT Exemplar · Class 9 Mathematics Polynomials

72 questions · 72 still being checked

EXERCISE 2.1 1–10 (part 1 of 8)

  1. Write the correct answer in each of the following :

    Exercise 1

    Which one of the following is a polynomial? (A) x22−2x2\displaystyle \frac{x^{2}}{2}-\frac{2}{x^{2}} (B) 2x−1\displaystyle \sqrt{2 x}-1 (C) x2+3x32x\displaystyle x^{2}+\frac{3 x^{\frac{3}{2}}}{\sqrt{x}} (D) x−1x+1\displaystyle \frac{x-1}{x+1}

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    (C)
    (C) \(\displaystyle x^{2}+\dfrac{3x^{3/2}}{\sqrt{x}}\) reduces to a polynomial in \(\displaystyle x\).
    \[x^{2}+\frac{3x^{3/2}}{x^{1/2}} = x^{2}+3x^{\frac{3}{2}-\frac{1}{2}} = x^{2}+3x \]
    (A)
    has \(\displaystyle x^{-2}\); (B) has \(\displaystyle x^{1/2}\) -- a negative and a fractional power of \(\displaystyle x\), which a polynomial forbids. (D) is a quotient by the non-constant polynomial \(\displaystyle x+1\).

  2. Exercise 2

    2\displaystyle \sqrt{2} is a polynomial of degree (A) 2\displaystyle 2 (B) 0\displaystyle 0 (C) 1\displaystyle 1 (D) 12\displaystyle \frac{1}{2}

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    (B)
    (B) \(\displaystyle 0\). \[\sqrt{2} = \sqrt{2}\,x^{0} \] A nonzero constant is a polynomial of degree \(\displaystyle 0\).

  3. Exercise 3

    Degree of the polynomial 4x4+0x3+0x5+5x+7\displaystyle 4 x^{4}+0 x^{3}+0 x^{5}+5 x+7 is (A) 4\displaystyle 4 (B) 5\displaystyle 5 (C) 3\displaystyle 3 (D) 7\displaystyle 7

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    (A)
    (A) \(\displaystyle 4\). \[4x^{4}+0x^{3}+0x^{5}+5x+7 = 4x^{4}+5x+7 \] Terms with zero coefficient vanish; the highest surviving power of \(\displaystyle x\) is \(\displaystyle 4\).

  4. Exercise 4

    Degree of the zero polynomial is (A) 0\displaystyle 0 (B) 1\displaystyle 1 (C) Any natural number (D) Not defined

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    (D)
    (D) Not defined. The zero polynomial has no term with a nonzero coefficient, so no highest power of \(\displaystyle x\) exists to call its degree.

  5. Exercise 5

    If p(x)=x2−22x+1\displaystyle p(x)=x^{2}-2 \sqrt{2} x+1, then p(22)\displaystyle p(2 \sqrt{2}) is equal to (A) 0\displaystyle 0 (B) 1\displaystyle 1 (C) 42\displaystyle 4 \sqrt{2} (D) 82+1\displaystyle 8 \sqrt{2}+1

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    (B)
    (B) \(\displaystyle 1\). \[p(2\sqrt{2}) = (2\sqrt{2})^{2} - 2\sqrt{2}\cdot(2\sqrt{2}) + 1 \] \[= 8 - 8 + 1 = 1 \]

  6. Exercise 6

    The value of the polynomial 5x−4x2+3\displaystyle 5 x-4 x^{2}+3, when x=−1\displaystyle x=-1 is (A) - 6\displaystyle 6 (B) 6\displaystyle 6 (C) 2\displaystyle 2 (D) -2\displaystyle 2

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    (A)
    (A) \(\displaystyle -6\). \[5(-1) - 4(-1)^{2} + 3 = -5 - 4 + 3 = -6 \]

  7. Exercise 7

    If p(x)=x+3\displaystyle p(x)=x+3, then p(x)+p(−x)\displaystyle p(x)+p(-x) is equal to (A) 3\displaystyle 3 (B) 2x\displaystyle 2 x (C) 0\displaystyle 0 (D) 6\displaystyle 6

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    (D)
    (D) \(\displaystyle 6\). \[p(x)+p(-x) = (x+3)+(-x+3) = 6 \]

  8. Exercise 8

    Zero of the zero polynomial is (A) 0\displaystyle 0 (B) 1\displaystyle 1 (C) Any real number (D) Not defined

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    (C)
    (C) Any real number. \[p(x) = 0 \quad \text{for every } x \] The zero polynomial vanishes at every value of \(\displaystyle x\), so each real number is a zero of it.

  9. Exercise 9

    Zero of the polynomial p(x)=2x+5\displaystyle p(x)=2 x+5 is (A) −25\displaystyle -\frac{2}{5} (B) −52\displaystyle -\frac{5}{2} (C) 25\displaystyle \frac{2}{5} (D) 52\displaystyle \frac{5}{2}

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    (B)
    (B) \(\displaystyle -\dfrac{5}{2}\). \[2x+5 = 0 \implies x = -\frac{5}{2} \]

  10. Exercise 10

    One of the zeroes of the polynomial 2x2+7x−4\displaystyle 2 x^{2}+7 x-4 is (A) 2\displaystyle 2 (B) 12\displaystyle \frac{1}{2} (C) −12\displaystyle -\frac{1}{2} (D) -2\displaystyle 2

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    (B)
    (B) \(\displaystyle \dfrac{1}{2}\). \[2x^{2}+7x-4 = (2x-1)(x+4) \] \[2x-1=0 \implies x=\frac{1}{2} \]