Polynomials: 1 mark Questions (CBSE Class 10)

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 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

If the zeroes of the polynomial $p(x)=2x^2-7x+6$ are $\alpha$ and $\beta$, then the value of $\frac{1}{\alpha }+\frac{1}{\beta }$ is

1. (A)$\frac{7}{2}$
2. (B)$\frac{6}{7}$
3. (C)$\frac{-7}{6}$
4. (D)$\frac{7}{6}$

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.

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

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

How many zeroes does p(x) = (x - 2) (x + 3) have ?

1. (A)Zero
2. (B)One
3. (C)Two
4. (D)Three

The sum and product of zeroes of a quadratic polynomial p(x) are $\frac{-1}{3}$ and 2 respectively. The polynomial p(x) is :

1. (A)$3x^2-x+6$
2. (B)$x^2+\frac{1}{3}x-2$
3. (C)$3x^2-x+2$
4. (D)$-3x^2-x-6$

A polynomial p(x), which has sum of its zeroes equal to their product, is :

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

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

Observe the graph of polynomial $p(x)$. The zeroes of the polynomial are

1. (A)$-2$, 0, 2.5
2. (B)$-2$, 2.5
3. (C)0, 4
4. (D)$-2$, 0

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)$x^2-24$

If sum and product of zeroes of a polynomial are $(-3)$ and $(-2)$ respectively, then a polynomial is

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

One of the zeroes of the polynomial $p(x)=k{x}^2-9x+3$ is $\left(-\frac{3}{2}\right)$. The value of $k$ is :

1. (A)$\frac{22}{3}$
2. (B)$-\frac{14}{3}$
3. (C)$\frac{14}{3}$
4. (D)$-\frac{22}{3}$

$\alpha ,\beta$ are zeroes of the polynomial $2x^2+5x+1$. The value of $\left(\frac{1}{\alpha }+\frac{1}{\beta }\right)$ is :

1. (A)$-\frac{5}{4}$
2. (B)5
3. (C)$\frac{5}{4}$
4. (D)$-5$

In the given figure, graph of $p(x)$ is shown. Number of distinct zeroes of $p(x)$ is :

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

If $\alpha ,\beta$ are zeroes of the polynomial $3x^2+14x-5$, then the value of $3\left(\frac{\alpha +\beta }{\alpha \beta }\right)$ is :

1. (A)$\frac{14}{5}$
2. (B)$\frac{42}{5}$
3. (C)$-\frac{14}{5}$
4. (D)$-\frac{42}{5}$

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)$(x+2{)}^2$

In the given figure, graph of polynomial $p(x)$ is shown. Number of zeroes of $p(x)$ is

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

A quadratic polynomial having zeroes 0 and $-$ 2, is

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

In the given graph, the polynomial $p(x)$ is shown. Number of zeroes of $p(x)$ is

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

If $\alpha$ and $\beta$ are the zeroes of polynomial $3x^2+6x+k$ such that $\alpha +\beta +\alpha \beta =-\frac{2}{3}$, then the value of $k$ is :

1. (A)$-8$
2. (B)$8$
3. (C)$-4$
4. (D)$4$

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)$4$

The sum of the zeroes of the polynomial $p(x)=5x-7x^2+3$ is :

1. (A)$\frac{-7}{5}$
2. (B)$\frac{7}{5}$
3. (C)$\frac{5}{7}$
4. (D)$\frac{-5}{7}$

If $-4$ is a zero of the polynomial $p(x)=x^2-x-(2+2k)$, then the value of k is :

1. (A)3
2. (B)9
3. (C)6
4. (D)$-9$

If one zero of the polynomial $q(x)=(p^2+4)x^2+65x+4p$ is reciprocal of the other, then the value of ‘$p$’ is :

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

If $\alpha$ and $\beta$ are the zeroes of the polynomial $p(x)=x^2-ax-b$, then the value of $(\alpha +\beta +\alpha \beta )$ is equal to :

1. (A)$a+b$
2. (B)$-a-b$
3. (C)$a-b$
4. (D)$-a+b$

Zeroes of the polynomial $p(x)=x^2-3\sqrt{2}x+4$ are :

1. (A)$2,\sqrt{2}$
2. (B)$2\sqrt{2},\sqrt{2}$
3. (C)$4\sqrt{2},-\sqrt{2}$
4. (D)$\sqrt{2},2$

Zeroes of the polynomial $p(y)=7y^2-\frac{11}{3}y-\frac{2}{3}$ are :

1. (A)$-\frac{2}{3},-\frac{1}{7}$
2. (B)$-\frac{2}{7},-\frac{1}{3}$
3. (C)$\frac{2}{3},\frac{1}{7}$
4. (D)$\frac{2}{3},-\frac{1}{7}$

If $\alpha$ and $\beta$ are zeroes of the polynomial $p(x)=k{x}^2-30x+45k$ and $\alpha +\beta =\alpha \beta$, then the value of 'k' is :

1. (A)$-\frac{2}{3}$
2. (B)$-\frac{3}{2}$
3. (C)$\frac{3}{2}$
4. (D)$\frac{2}{3}$

Which of the following statements is true for a polynomial $p(x)$ of degree 3?

1. (A)$p(x)$ has at most two distinct zeroes.
2. (B)$p(x)$ has at least two distinct zeroes.
3. (C)$p(x)$ has exactly three distinct zeroes.
4. (D)$p(x)$ has at most three distinct zeroes.

If the zeroes of the polynomial $a{x}^2+bx+\frac{2a}{b}$ are reciprocal of each other, then the value of $b$ is

1. (A)2
2. (B)$\frac{1}{2}$
3. (C)$-2$
4. (D)$-\frac{1}{2}$

If one of the zeroes of the quadratic polynomial $(\alpha -1)x^2+\alpha x+1$ is $-3$, then the value of $\alpha$ is :

1. (A)$-\frac{2}{3}$
2. (B)$\frac{2}{3}$
3. (C)$\frac{4}{3}$
4. (D)$\frac{3}{4}$

For what value of $k$, the product of zeroes of the polynomial $k{x}^2-4x-7$ is 2 ?

1. (A)$-\frac{1}{14}$
2. (B)$-\frac{7}{2}$
3. (C)$\frac{7}{2}$
4. (D)$-\frac{2}{7}$

Assertion (A) : Zeroes of a polynomial $p(x)=x^2-2x-3$ are $-1$ and 3.
Reason (R) : The graph of polynomial $p(x)=x^2-2x-3$ intersects $x$-axis at $(-1,0)$ and $(3,0)$.

1. (A)Both, Assertion (A) and Reason (R) are true. Reason (R) explains Assertion (A) completely.
2. (B)Both, Assertion (A) and Reason (R) are true. Reason (R) does not explain Assertion (A).
3. (C)Assertion (A) is true but Reason (R) is false.
4. (D)Assertion (A) is false but Reason (R) is true.

A quadratic polynomial, the sum of whose zeroes is $-5$ and their product is 6, is

1. (A)$x^2+5x+6$
2. (B)$x^2-5x+6$
3. (C)$x^2-5x-6$
4. (D)$-x^2+5x+6$

The zeroes of the polynomial $3x^2+11x-4$ are :

1. (A)$\frac{1}{3},4$
2. (B)$\frac{-1}{3},-4$
3. (C)$\frac{1}{3},-4$
4. (D)$\frac{-1}{3},4$

The zeroes of the polynomial $3x^2-5x-2$, are :

1. (A)$\frac{1}{3},2$
2. (B)$\frac{-1}{3},2$
3. (C)$\frac{-1}{3},-2$
4. (D)$\frac{1}{3},-2$

The zeroes of the polynomial $3x^2+8x-3$ are :

1. (A)$\frac{1}{3},3$
2. (B)$\frac{1}{3},-3$
3. (C)$\frac{-1}{3},3$
4. (D)$\frac{-1}{3},-3$

A quadratic polynomial whose zeroes are 3 and $-2$, is :

1. (A)$x^2-x-6$
2. (B)$x^2+x-6$
3. (C)$2x^2-x-12$
4. (D)$x^2+x+6$

In the given figure, graph of a polynomial $f(x)$ is shown. The number of zeroes of polynomial $f(x)$ is :

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

A quadratic polynomial whose zeroes are $-8$ and 3, is

1. (A)$(x+8)(x+3)$
2. (B)$x^2+5x+24$
3. (C)$(x-8)(x-3)$
4. (D)$x^2+5x-24$

If the two zeroes of a quadratic polynomial are $\pm \sqrt{5}$, then the quadratic polynomial is :

1. (A)$x^2+5$
2. (B)$(x+\sqrt{5}{)}^2$
3. (C)$4(x^2-5)$
4. (D)$x^2-\sqrt{5}$

If one zero of a quadratic polynomial $k{x}^2+4x+k$ is 1, then the value of $k$ is :

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

The number of quadratic polynomials having zeroes $-1$ and 3 is :

1. (A)1
2. (B)2
3. (C)3
4. (D)more than 3

What should be added to the polynomial $x^2-5x+4$, so that 3 is a zero of the resulting polynomial ?

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

If the sum of zeroes of the polynomial $p(x)=2x^2-k\sqrt{2}x+1$ is $\sqrt{2}$, then value of $k$ is :

1. (A)$\sqrt{2}$
2. (B)2
3. (C)$2\sqrt{2}$
4. (D)$\frac{1}{2}$

The zeroes of a polynomial $x^2+px+q$ are twice the zeroes of the polynomial $4x^2-5x-6$. The value of $p$ is :

1. (A)$-\frac{5}{2}$
2. (B)$\frac{5}{2}$
3. (C)$-5$
4. (D)10

Assertion (A) : If the graph of a polynomial touches $x$-axis at only one point, then the polynomial cannot be a quadratic polynomial.
Reason (R) : A polynomial of degree $n(n>1)$ can have at most $n$ zeroes.

1. (A)Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
2. (B)Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for 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 the sum and the product of zeroes of a quadratic polynomial are $2\sqrt{3}$ and 3 respectively, then a quadratic polynomial is :

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

If $\alpha ,\beta$ are the zeroes of the polynomial $6x^2-5x-4$, then $\frac{1}{\alpha }+\frac{1}{\beta }$ is equal to :

1. (A)$\frac{5}{4}$
2. (B)$-\frac{5}{4}$
3. (C)$\frac{4}{5}$
4. (D)$\frac{5}{24}$

If $\alpha$ and $\beta$ are zeroes of the polynomial $5x^2+3x-7$, the value of $\frac{1}{\alpha }+\frac{1}{\beta }$ is

1. (A)$-\frac{3}{7}$
2. (B)$\frac{3}{5}$
3. (C)$\frac{3}{7}$
4. (D)$-\frac{5}{7}$

If $\alpha$ and $\beta$ are zeroes of the polynomial $2x^2-9x+5$, then value of ${\alpha }^2+{\beta }^2$ is

1. (A)$\frac{1}{4}$
2. (B)$\frac{61}{4}$
3. (C)1
4. (D)$\frac{71}{4}$

If $\alpha$ and $\beta$ $(\alpha >\beta )$ are the zeroes of the polynomial $-x^2+8x+9$, then $(\alpha -\beta )$ is equal to

1. (A)$-10$
2. (B)10
3. (C)$\pm 10$
4. (D)8

The zeroes of the quadratic polynomial $2x^2-3x-9$ are :

1. (A)$3,\frac{-3}{2}$
2. (B)$-3,\frac{-3}{2}$
3. (C)$-3,\frac{3}{2}$
4. (D)$3,\frac{3}{2}$

What should be subtracted from the polynomial $x^2-16x+30$, so that 15 is the zero of the resulting polynomial ?

1. (A)30
2. (B)14
3. (C)15
4. (D)16

What should be added from the polynomial $x^2-5x+4$, so that 3 is the zero of the resulting polynomial ?

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

If a polynomial $p(x)$ is given by $p(x)=x^2-5x+6$, then the value of $p(1)+p(4)$ is :

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

A quadratic polynomial, one of whose zeroes is $2+\sqrt{5}$ and the sum of whose zeroes is 4, is :

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

The ratio of the sum and product of the roots of the quadratic equation $5x^2-6x+21=0$ is :

1. (A)5 : 21
2. (B)2 : 7
3. (C)21 : 5
4. (D)7 : 2

If $\alpha$ and $\beta$ are the zeroes of the polynomial $p(x)=k{x}^2-30x+45k$ and $\alpha +\beta =\alpha \beta$, then the value of $k$ is :

1. (A)$-\frac{2}{3}$
2. (B)$-\frac{3}{2}$
3. (C)$\frac{3}{2}$
4. (D)$\frac{2}{3}$

Assertion (A) : Degree of a zero polynomial is not defined.
Reason (R) : Degree of a non-zero constant polynomial is 0.

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

The graph of $y=p(x)$ is shown in the figure for some polynomial $p(x)$. The number of zeroes of $p(x)$ is/are :

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

The sum and the product of zeroes of the polynomial $p(x)=x^2+5x+6$ are respectively

1. (A)$5,-6$
2. (B)$-5,6$
3. (C)2, 3
4. (D)$-2,-3$

The zeroes of the polynomial $p(x)=x^2+3x+2$ are given as.

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

The graph of $y=f(x)$ is shown in the figure for some polynomial $f(x)$.
The number of zeroes of $f(x)$ is

1. (A)5
2. (B)6
3. (C)4
4. (D)8

The sum and product of zeroes of the polynomial $p(x)=3x^2-5x+2$ are

1. (A)$\frac{5}{3},\frac{2}{3}$
2. (B)$\frac{-5}{3},\frac{2}{3}$
3. (C)$1,\frac{2}{3}$
4. (D)$\frac{-5}{3},\frac{-2}{3}$

Graph of a polynomial p(x) is given in the figure. The number of zeroes of p(x) is :

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

Assertion (A) : Polynomial $x^2+4x$ has two real zeroes.
Reason (R) : Zeroes of the polynomial $x^2+ax$ $(a\ne 0)$ are 0 and a.

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.

A quadratic polynomial the sum and product of whose zeroes are $-3$ and 2 respectively, is :

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

If $p(x)=x^2+5x+6$, then $p(-2)$ is :

1. (A)20
2. (B)0
3. (C)$-8$
4. (D)8

A quadratic polynomial whose sum and product of zeroes are 2 and $-1$ respectively is :

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

The number of polynomials having zeroes $-3$ and 4 is :

1. (A)1
2. (B)2
3. (C)3
4. (D)more than 3

If one zero of the quadratic polynomial $k{x}^2+3x+k$ is 2, then the value of k is :

1. (A)$-\frac{6}{5}$
2. (B)$\frac{6}{5}$
3. (C)$\frac{5}{6}$
4. (D)$-\frac{5}{6}$

The graph of $y=f(x)$ is shown in the figure for some polynomial $f(x)$.
The number of zeroes of $f(x)$ is

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

The zeroes of the quadratic polynomial $16x^2-9$ are :

1. (A)$\frac{3}{4},\frac{3}{4}$
2. (B)$-\frac{3}{4},\frac{3}{4}$
3. (C)$\frac{9}{16},\frac{9}{16}$
4. (D)$-\frac{3}{4},-\frac{3}{4}$

The zeroes of the polynomial $p(x)=25x^2-49$ are :