Class 10 Maths · Chapter 2

Polynomials

58 Class 10 Maths questions on Polynomials from the NCERT textbook, NCERT Exemplar and CBSE board papers 2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 2 of 3

1. Q21 Exemplar · Exercise 2.3
   Find the zeroes of the ​following polynomials ​by factorisation ​method and ​verify the relations ​between the zeroes and the coefficients ​of the ​polynomials: $2x^2+\frac{7}{2}x+\frac{3}{4}$
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   The zeroes of $2x^2+\frac{7}{2}x+\frac{3}{4}$ are $x=-\frac{3}{2}$ and $x=-\frac{1}{4}$. Verified: sum of zeroes $=-\frac{3}{2}-\frac{1}{4}=-\frac{7}{4}=-\frac{b}{a}$, and product of zeroes $=\left(-\frac{3}{2}\right)\times \left(-\frac{1}{4}\right)=\frac{3}{8}=\frac{c}{a}$.

   Step-by-step solution →
2. Q22 Exemplar · Exercise 2.3
   Find the ​zeroes of the following polynomials by factorisation method and ​verify the ​relations between the zeroes ​and the coefficients ​of ​the ​polynomials: $4x^2+5\sqrt{2}x-3$
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   The zeroes of $4x^2+5\sqrt{2}x-3$ are $x=-\frac{3\sqrt{2}}{2}$ and $x=\frac{\sqrt{2}}{4}$. Verified: sum of zeroes $=-\frac{3\sqrt{2}}{2}+\frac{\sqrt{2}}{4}=-\frac{5\sqrt{2}}{4}=-\frac{b}{a}$, and product of zeroes $=\left(-\frac{3\sqrt{2}}{2}\right)\times \frac{\sqrt{2}}{4}=-\frac{3}{4}=\frac{c}{a}$.

   Step-by-step solution →
3. Q23 Exemplar · Exercise 2.3
   Find ​the ​zeroes of the following polynomials by ​factorisation ​method and verify ​the ​relations between the zeroes ​and the ​coefficients of the polynomials: $2s^2-(1+2\sqrt{2})s+\sqrt{2}$
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   The zeroes are $s=\frac{1}{2}$ and $s=\sqrt{2}$. Verification: sum of zeroes $=\frac{1}{2}+\sqrt{2}=\frac{1+2\sqrt{2}}{2}=-\frac{b}{a}$ and product of zeroes $=\frac{1}{2}\times \sqrt{2}=\frac{\sqrt{2}}{2}=\frac{c}{a}$.

   Step-by-step solution →
4. Q24 Exemplar · Exercise 2.3
   Find the ​zeroes of the following polynomials ​by factorisation method and ​verify the ​relations between the ​zeroes and the ​coefficients of the polynomials: $v^2+4\sqrt{3}v-15$
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   The zeroes are $v=\sqrt{3}$ and $v=-5\sqrt{3}$. Verification: sum of zeroes $=\sqrt{3}-5\sqrt{3}=-4\sqrt{3}=-\frac{b}{a}$ and product of zeroes $=\sqrt{3}\times (-5\sqrt{3})=-15=\frac{c}{a}$.

   Step-by-step solution →
5. Q25 Exemplar · Exercise 2.3
   Find the ​zeroes of the following ​polynomials ​by factorisation method ​and verify the ​relations between the zeroes and the coefficients of the polynomials: $y^2+\frac{3}{2}\sqrt{5}y-5$
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   The zeroes are $y=-2\sqrt{5}$ and $y=\frac{\sqrt{5}}{2}$. Verification: sum of zeroes $=-2\sqrt{5}+\frac{\sqrt{5}}{2}=-\frac{3\sqrt{5}}{2}=-\frac{b}{a}$ and product of zeroes $=(-2\sqrt{5})\times \frac{\sqrt{5}}{2}=-5=\frac{c}{a}$.

   Step-by-step solution →
6. Q26 Exemplar · Exercise 2.3
   Find the zeroes ​of the following polynomials by factorisation method and ​verify the relations ​between ​the zeroes and ​the coefficients of the ​polynomials: $7y^2-\frac{11}{3}y-\frac{2}{3}$
   Show answer

   The zeroes are $y=\frac{2}{3}$ and $y=-\frac{1}{7}$. Verification: sum of zeroes $=\frac{2}{3}-\frac{1}{7}=\frac{11}{21}=-\frac{b}{a}$ and product of zeroes $=\frac{2}{3}\times \left(-\frac{1}{7}\right)=-\frac{2}{21}=\frac{c}{a}$.

   Step-by-step solution →
7. Q27 CBSE 2026
   At which of ​the ​following ​points, ​the ​quadratic polynomial $p(x)=-3x+18x^2-1$ intersects the ​positive $x$-axis ​?

   1. (a)$\left(\frac{1}{6},0\right)$
   2. (b)$\left(-\frac{1}{3},0\right)$
   3. (c)$\left(-\frac{1}{6},0\right)$
   4. (d)$\left(\frac{1}{3},0\right)$
   Show answer

   (d) $\left(\frac{1}{3},0\right)$

   Step-by-step solution →
8. Q28 CBSE 2026
   If $\alpha$ and $\beta$ are two ​zeroes ​of ​the ​quadratic polynomial $p(x)=x^2-11x+30$, then $\frac{1}{\alpha }+\frac{1}{\beta }$ ​is equal to:

   1. (a)$\frac{30}{11}$
   2. (b)$\frac{11}{30}$
   3. (c)$-\frac{11}{30}$
   4. (d)$-\frac{30}{11}$
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   (b) $\frac{11}{30}$

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9. Q29 CBSE 2026
   The graph of a quadratic ​polynomial $f(x)$ passes through $(5,0)$, $(0,-1)$ ​and $(-2,0)$. ​The two ​factors of ​the ​polynomial ​are

   1. (a)$(x+2),(x-5)$
   2. (b)$(x+5),(x-2)$
   3. (c)$(x+1),(x-5)$
   4. (d)$(x-1),(x+2)$
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   (a) $(x+2),(x-5)$

   Step-by-step solution →
10. Q30 CBSE 2026
    If the zeroes ​of a ​polynomial $p(x)$ are $-3$ ​and $8$, ​then $p(x)$ ​equals

    1. (a)$x^2+5x-4$
    2. (b)$(x+3)(-x+8)$
    3. (c)$a(x^2+5x-24)$
    4. (d)$x^2-24$
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    (b) $(x+3)(-x+8)$

    Step-by-step solution →
11. Q31 CBSE 2026
    The ​graph of $y=f(x)$ is ​given. ​The ​number of ​zeroes of $f(x)$ ​is :

    1. (a)$0$
    2. (b)$1$
    3. (c)$2$
    4. (d)$4$
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    (a) $0$

    Step-by-step solution →
12. Q32 CBSE 2026
    The ​graph ​of $y=f(x)$ ​is given. ​The number ​of ​distinct zeroes of $y=f(x)$ is :

    1. (a)$0$
    2. (b)$1$
    3. (c)$2$
    4. (d)$3$
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    (c) $2$

    Step-by-step solution →
13. Q33 CBSE 2026
    If $\alpha$ and $\beta$ are two ​zeroes ​of ​a polynomial $f(x)=p{x}^2-2x+3p$ ​and $\alpha +\beta =\alpha \beta$, then value of $p$ ​is :

    1. (a)$-\frac{2}{3}$
    2. (b)$\frac{2}{3}$
    3. (c)$\frac{1}{3}$
    4. (d)$-\frac{1}{3}$
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    (b) $\frac{2}{3}$

    Step-by-step solution →
14. Q34 CBSE 2026
    Observe the ​graph of polynomial $p(x)$. ​Number ​of zeroes of $p(x)$ ​is

    1. (a)$5$
    2. (b)$4$
    3. (c)$6$
    4. (d)$3$
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    (d) $3$

    Step-by-step solution →
15. Q35 CBSE 2026
    The ​graph of polynomial $p(x)=k$ is ​shown here. ​Number of ​zeroes of polynomial $p(x)$ ​is ​:

    1. (a)$0$
    2. (b)$1$
    3. (c)$2$
    4. (d)infinitely many
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    (a) $0$

    Step-by-step solution →
16. Q36 CBSE 2026
    The ​graph of ​a polynomial $p(x)$ is ​shown here. ​The number ​of zeroes ​of the polynomial $p(x)$ ​is

    1. (a)$5$
    2. (b)$1$
    3. (c)$0$
    4. (d)$4$
    Show answer

    (d) $4$

    Step-by-step solution →
17. Q37 CBSE 2026
    The graph ​of a quadratic ​polynomial ​is ​shown in the figure. ​The sum and product ​of zeroes ​of the polynomial respectively are :

    1. (a)$2$ and $3$
    2. (b)$2$ and $-3$
    3. (c)$-2$ and $3$
    4. (d)$-2$ and $-3$
    Show answer

    (b) $2$ and $-3$

    Step-by-step solution →
18. Q38 CBSE 2026
    Which of ​the following graphs represents a ​polynomial ​with ​both zeroes being positive ?

    1. (a)Graph (a)
    2. (b)Graph (b)
    3. (c)Graph (c)
    4. (d)Graph (d)
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    (c) Graph (c)

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19. Q39 CBSE 2026
    In which of the following graphs of ​the polynomials is one ​of ​the ​zeroes ​twice the other ?

    1. (a)(i) only
    2. (b)(i) and (ii)
    3. (c)(ii) and (iii)
    4. (d)(ii) only
    Show answer

    (d) (ii) only

    Step-by-step solution →
20. Q40 CBSE 2026
    The value of $k$ ​for which ​sum ​of the zeroes of ​the ​polynomial $p(x)=3x^2-kx+6$ is $2$, is

    1. (a)$2$
    2. (b)$-6$
    3. (c)$-2$
    4. (d)$6$
    Show answer

    (d) $6$

    Step-by-step solution →