November 20, 2024

Polynomials Worksheet Grade 9 with PDF

by Bina singhJanuary 5, 2021May 26, 2022

Polynomials Worksheet

1. Which of the following is a true statement?

(a) $5x^{3}$ is a monomial (b) $x^{2}+5x-3$

is a linear polynomial

(c) x+1 is monomial (d) $x^{2}+4x-1$ is a binomial

2. A quadratic polynomial whose product and sum of zeroe are $\frac{1}{3}$

and $\sqrt{2}\, \,$ respectively.

(a) $3x^{2}-x+3\sqrt{2}\, \, x$

(b) $3x^{2}-3\sqrt{2 }\, \, x+1$

(c) $3x^{2}+x-3\sqrt{2}\, \, x$

(d) $3x^{2}+3\sqrt{2}\, \, x+1$

3. If α , β are the zeros of the polynomial $f(x)=ax^{2}+bx+c,$

then = $\frac{1}{\alpha ^{2}}+\frac{1}{\beta ^{2}}$

(a) $\frac{b^{2}+2ac}{c^{2}}$

(b) $\frac{b^{2}-2ac}{c^{2}}$

(c) $\frac{b^{2}+2ac}{a^{2}}$

(d) $\frac{b^{2}-2ac}{a^{2}}$

4. The number of zeroes of a cubic polynomial is

(a) at most 3 (b) 3

(c) at least 3 (d) 2

5. If $a-b$

, $a$ and $a+b$

are zeros of the polynomial $x^{3}-3x^{2}+x+1$ , then the value of $a+b$

is

(a) $-1-\sqrt{2}$ (b) 3

(c) $-1+\sqrt{2}$

(d) $1\pm \sqrt{2}$

6. The number of polynomials having zeros as -2 and 5 is

(a) 1 (b)2

(c)3 (d) more than 3

7. If the sum of the zeros of the quadratic polynomial for $kx^{2}+2x+3k$

is equal to the product of its zeros then $k$ =?

(a) $\frac{1}{3}$

(b) $\frac{2}{3}$

(c) $-\frac{2}{3}$

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

8. The zeroes of the quadratic polynomial $x^{2}+99x+127$

are

(a) both negative (b) one positive and one negative

( c) both positive (d) both equal

9. The polynomial to be added to the polynomial $x^{4}+2x^{3}-2x^{2}+x-1$ so that the resulting polynomial is exactly divisible by $x^{2}+2x-3$

is

(a) $x^{2}+1$ (b) $2-x$

(c) $x-2$ (d)x+2

10. Find a quadratic polynomial whose one zero is -5 and product of zeroes is 0.

11. $p(x)=g(x)q(x)+r(x)$

. If degree of $g(x)$ =4, degree of $q(x)=3$

and degree of $r(x)=2$ , then find the degree of $p(x)$

.

12. Find the sum of the zeroes of the given quadratic polynomial $-3x^{2}+k$

13. Divide $15y^{4}-16y^{3}+9y^{2}-\frac{10}{3}\, \, y$

by $3y-2$ .

14. Verify that $x=3$

is a zero of the polynomial $p(x)=2x^{3}-5x^{2}-4x+3$ .

15. If α and β are the zeros of the polynomial $f(x)=x^{2}+x-2$

, find the value of . $(\frac{1}{\alpha }-\frac{1}{\beta })$

Answers. 1. (a) 2. (b) 3. (b) 4. (a) 5.(d) 6. (d) 7. (c) 8. (a) 9. (c) 10. $x^{2}+5x$

11. 7 12. 0 13. quotient : $5y^{3}-2y^{2}+\frac{5}{3}\, \, y$ and remainder=0 15. $-\frac{3}{2}$

Download PDF Polynomial(worksheet-1).pdf

Bina singh

View all posts by Bina singh →

Leave a Reply Cancel reply