Polynomials: CBSE Class 10 Previous Year Questions

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

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

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

Assertion (A) : The polynomial $p(y)=y^2+4y+3$ has two zeroes.
Reason (R) : A quadratic polynomial can have at most two zeroes.

1. (A)Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

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)$-\frac{1}{3}$

During a theatre drama, a backdrop of building arches was used. The shape of the curve shown below can be represented by the polynomial $p(x)=-x^2+2x+8$, where $x$ is the length (in feet) on stage level.
Based on the figure given above, answer the following questions :
(i) Determine the height of the arch. (1)
(ii) (a) Find zeroes of the polynomial p(x). Which points on the graph represent the zeroes ? (2)
OR (ii) (b) Find the span of the arch on the stage floor. (2)
(iii) Write the coordinates of the point of intersection of the above curve with the y-axis. (1)

An arch of a railway bridge, built on Chenab riverbed, is shown in the above diagram. It is a parabolic arch connecting two hills at P and Q. If the parabolic curve is represented by the polynomial $p(x)=-0.0025x^2-0.025x+136$.
Observe the diagram and based on above information, answer the following questions :
(i) Write the co-ordinates of point A. (1)
(ii) Find the span of the arch. (1)
(iii) (a) Write the zeroes of the polynomial using diagram and verify the relationship between sum of zeroes and polynomials. (2)
OR (iii) (b) Find the values of $p(x)$ at $x=100$ and $x=-100$. Are they same ? (2)

Observe the given graph of polynomial p($x$). The number of zeroes of p($x$) is

1. (A)0
2. (B)1
3. (C)3
4. (D)2

A quadratic polynomial having only zero (–2) is

1. (A)$(x-2{)}^2$
2. (B)$x^2-2$
3. (C)$x^2+2x$
4. (D)$(x+2{)}^2$

Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is :

1. (A)$3$
2. (B)$5$
3. (C)$2$
4. (D)$4$