June 13, 2024

Polynomials Worksheet Grade 9 with PDF

                                                           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


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