Class 10 Polynomial Test paper

1. If x=1 is a zero of a polynomial f(x) = x³-2x²+4x+k. Write the value of k                        (Ans. k= -3)

2. For what value of k , -4 is a zero of the p(x)=. x² – x - (2k+2) ?  (Ans. = 9)

3. Verify whether 3 and 2 are the zeros of the poly. (x - 2)(x -3)?

4. Find the zeros of the polynomial f(x) =4x²+8x               (Ans. 0, -2)

5. Find a quadratic polynomial each with the given zeros as sum and the product of its zeros respectively      

(a) ¼, -1              (b) √2  , 1/3                                       
{Ans.(a).4x²-x-4,(b) 3x²-3√2 x+1}

3 marks questions

1. Using division algorithm, find the quotient and the remainder on dividing f(x) by g(x) , where

f(x) =6x³ +13x² + x - 2 and g(x) =2x+1                                              

[Ans.q (x) =3x²+5x-2, r(x)=0]

2. If α , β are the zeros of 2y2+7y+5 write the value of α+ β +α β.   
(Ans. -1)

3. Find the zeros of a quadratic polynomial 5x2-4-8x and verify the relationship between the zeros and the coefficients of the polynomial.                                                                                            (Ans.2,-2/5 )

4. If α, β are the zeros of the poly. f(x)=x²-px+q, find the value of  (a) α²+β²       (b)1/α +1β        

(Ans. P² -2q, p/q ) 

5. On dividing x³+2x²-5x-6 by a polynomial g(x) the quotient and remainder were x+1 and - 4x -4 respectively Find the polynomial g(x)      

(Ans. x²+ x - 2)

6. If (x + a) is a factor of 2x²+2ax+5x+10. Find a.              (Ans. a = 2)

7. Find all the zeros of 2x⁴-9x³+5x²+3x-1, if two of its zeros are 2+√3 & 2- √3

8. If the polynomial 6x⁴ + 8x³ + 17x² + 21x + 7 is divided by another polynomial 3x² + 4x + 1, the remainder comes out to be (ax + b), find a and b.

9. Find all other zeroes of the polynomial p(x) = 2x³ + 3x² – 11x – 6, if one of its zero is –3.

10. If one zero of the polynomial (a² +9)x² +13x +6a is reciprocal of the other . Find the value of a.

CBSE Class 10 Self Evaluation Tests for chapter Polynomial

Section-A

1. The zeroes of the quadratic polynomial x² + 99x + 127 are

(A) both positive (B) both negative (C) one positive and one negative (D) both equal

2. The zeroes of the quadratic polynomial x² + k x + k, k ≠ 0,

(A) cannot both be positive (B) cannot both be negative (C) are always unequal (D) are always equal

3. If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then

(A) c and a have opposite signs (B) c and b have opposite signs (C) c and a have the same sign (D) c and b have the same sign

4. If one of the zeroes of a quadratic polynomial of the form x²+ax + b is the negative of the other, then it

(A) has no linear term and the constant term is negative.

(B) has no linear term and the constant term is positive.

(C) can have a linear term but the constant term is negative.

(D) can have a linear term but the constant term is positive.

5. The number of polynomials having zeroes as –2 and 5 is

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

Section-B

1. Find the zeroes of 2x³ – 11x² + 17x – 6.

 2. Find the quadratic polynomial, the sum and the product of whose zeroes are ¹/₂, and –2 .

 3. Find the values of m and n for which x = 2 and –3 are zeroes of the polynomial:
 3x² – 2mx + 2n.

 4. Check whether x² + 4 is factor of x⁴ + 9x² + 20

Section-C

 5. Divide the polynomial (x⁴ + 1) by (x – 1) and verify the division algorithm.

 6. Find all zeroes of x⁴ – 3x³ – 5x² + 21x – 14, if two of its zeroes are √7 and – √7 

 7. On dividing x³ – 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4 respectively, find g(x). 

Section-D

8. Given that √2 is a zero of the cubic polynomial 6x³ + √2 x² – 10x – 4 √2 , find  its other two zeroes.

9. Find k so that x² + 2x + k is a factor of 2x⁴ + x³ – 14 x² + 5x + 6. Also find all the zeroes of the two polynomials.

10. Given that x – √5 is a factor of the cubic polynomial x³ – 3√ 5x² + 13x – 3 √5 , find all the zeroes of the polynomial.

10th maths Chapter Polynomial extrascore questions

Math Adda  

Chapter: POLYNOMIALS        

LEVEL-I

1. The zeroes of the polynomial 2x²-3x-2 are

a. 1, 2        b. -1/2,1    

c. ½,-2      d. -1/2,2                       [Ans- (d)]

2. If a and b are zeroes of the polynomial 2x²+7x-3, then the value of a² +b² is

a. 49/4                b. 37/4       

c. 61/4                d. 61/2                                                      
Ans-( c ) 

3. If the polynomial 6x³+16x²+px -5 is exactly divisible by 3x+ 5 , then the value of p is

a. -7      b. -5     

c.5        d.7                                                                                  
[Ans- (d )]

4. If 2 is a zero of the polynomials 3x2+ax-14 and 2x3+bx2+x-2, then the value of 2 - 2b is

a. -1       b. 5         

c. 9       d. -9                         

[Ans-( c ) ]

5. A quadratic polynomial whose product and sum of zeroes are 1/3 and √2 respectively is

(a) 3x² – x +3√ 2 (b) 3x² + x - 3√2 (c) 3x² + 3√2x +1 (d) 3x² – 3√2x +1         
[ Ans: (d)]

LEVEL-II

1. If 1 is a zero of the polynomial p(x) = ax² -3(a-1) x -1, then find the value of a.       
Ans: a=1

2. For what value of k, (-4) is zero of the polynomial x² – x – (2k+2)?                          
Ans: k=9

3. Write a quadratic polynomial, the sum and product of whose zeroes are 3 and -2. 
Ans: x² -3x-2

4. Find the zeroes of the quadratic polynomial 2x²-9-3x and verify the relationship between the zeroes and the coefficients.                                   Ans: 3, -3/2

5. Write the polynomial whose zeroes are 2 +√3 and 2 - √3.          Ans: p(x)=x2-4x+1

LEVEL – III

1. Find all the zeroes of the polynomial 2x³+x²-6x-3, if two of its zeroes are -√3 and √3. 
Ans: x=-1/2

2. If the polynomial x⁴ + 2x³ + 8x²+12x+18 is divided by another polynomial x² + 5, the remainder comes out to be  px+q. 

Find the value of p and q.                                                         Ans:p=2,q=3

3. If the polynomial 6x⁴+8x³+17x²+21x+7 is divided by another polynomial 3x²+4x+1, the remainder  comes out to  be (ax+b), find a and b.                      Ans:a=1, b=2

4. If two zeroes of the polynomial f(x)= x³-4x²-3x+12 are √3 and -√3, then find its third zero. Ans: 4

5. If a, b are zeroes of the polynomial x²-2x-15 then form a quadratic polynomial whose zeroes are  (2a) and (2b).              Ans: x²-4x-60

LEVEL – IV

1. Find other zeroes of the polynomial p(x)=2x⁴ +7x³19x²-14x +30 if two of its zeroes are √2 and -
√2.

Ans: 3/2 and -5

2. Divide 30x⁴ +11x³-82x²-12x-48 by (3x² +2x-4) and verify the result by division algorithm.

3. If the polynomial 6x⁴ +8x³-5x²+ax+b is exactly divisible by the polynomial 2x²-5, then find the 
value of a and b.     
Ans: a = -2 0 , b = - 2 5

4. Obtain all other zeroes of 3x⁴ -15x³+13x²+25x-30, if two of its zeroes are and ±√5/3. 
Ans: 
±√5/3,3,2

5. If a, b are zeroes of the quadratic polynomial p(x)=kx²+4x+4 such that a² +b²=24, find the value 
of k.                                                                        
Ans: k=2/3 or k= -1

SELF EVALUATION

1. If a, b are zeroes of the quadratic polynomial ax²+bx+c then find (a) a/b +b/a (b) a² +b²

2. If a, b are zeroes of the quadratic polynomial ax²+bx+c then find the value of a² - b²

3. If a, b are zeroes of the quadratic polynomial ax²+bx+c then find the value of a³ +b³

4. What must be added to 6x⁵+5x⁴+11x³-3x²+x+5 so that it may be exactly divisible by 3x² -2x+4 ?

5. If the square of difference of the zeroes of the quadratic polynomial f(x)= x²+px+45 is equal to 144, 
find the value of p.

Practice paper for class 10 chapter-Polynomials

1. Every linear equation in two variables has ___ solution(s).

(a) No (b) one (c) two (d) infinitely many

2. For a pair to be consistent and dependent the pair must have

(a) no solution (b) unique solution (c) infinitely many solutions (d) none of these

3. Graph of every linear equation in two variables represents a ___

(a) point (b) straight line(c) curve (d) triangle

4. Each point on the graph of pair of two lines is a common solution of he lines in case of

(a) Infinitely many solutions (b) only one solution (c) no solution (d) none of these

5.The pair of linear equations is said to be inconsistent if they have

(a) only one solution (b) no solution (c) infinitely many solutions. (d) both a and c

6. Find the value of k so that the equations x + 2y = – 7, 2x + ky + 14 = 0 will represent coincident
lines.

7. Give linear equations which is coincident with 2 x + 3y - 4 = 0 Find the value of K so that the pair of linear equations :

(3 K + 1) x + 3y – 2 = 0

(K² + 1) x + (k–2)y – 5 = 0 is inconsistent.

8. Solve for x and y :

2^x + 3^y = 17

2^{x + 2} – 3 ^y+1 = 5.

9. The area of a rectangle remain the same if its length is increased by 7 cm and the breadth is decreased  by 3 cm. The area remains unaffected if length is decreased by 7 cm and the breadth is increased by 5 cm. Find length and breadth.

10. A no. consists of three digits whose sum is 17. The middle one exceeds the sum of other two by 1. If the digits are reversed, the no. is diminished by 396. Find the no.

CBSE NCERT MATH 10th Chapter 2 Polynomials Test paper

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Class 10 Polynomial CBSE test Paper O1

Math Adda 

Polynomials sample test paper 

1. The graph of y=f(x) is given below. Find the number of zeroes of f(x)

2. Write the zeroes of the polynomial x2 -2x + 4.

3. Find a quadratic polynomial, the sum and product of whose zeroes are 0 and 5 respectively.

4. Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively

5. If a andb are the zeros of the quadratic polynomial f(x)= x2-5x+4, find the value of 1/a + 1/b-2a b

6. Find the zeroes of the quadratic polynomial 4 √3 x2 + 5 x - 2 √3 and verify the relationship between the zeroes and the coefficients.

7. Find the zeroes of the quadratic polynomial 4u2 + 8u and verify the relationship between the zeroes and the coefficients

8. Find the quadratic polynomial, the sum and product of whose zeroes are √2 and √3 respectively.

9. If a and b are the zeros of the given quadratic polynomial f(x)= 5x2 - 7x + 1, find the value 1/a + 1/b

10. Find the zeroes of the polynomial x2 – 3 and verify the relationship between the zeroes and the
Coefficients

11. Find the remainder when p(x)= x3-6x2+2x-4 when divided by 1 - 2x.

12. Find the remainder when x51+51 is divided by (x+1).

13. Find all the integral zeros of x3 -3x2 - 2x + 6

14. Obtain all zeros of 3x4 + 6x3 - 2x2 - 10x - 5, if two of its zeros are √5/√3 and - √5/√3

15. If (x - 2) and [x – ½ ] are the factors of the polynomials qx2 + 5x + r prove that q = r

16. If the zeroes of the polynomial are 3x2 − 5x + 2 are a+ b and a- b, find a and b.

17. On dividing 2x2 + 3x + 1 by a polynomial g(x), the quotient and the remainder were 2x-1 and 3 respectively. Find g (x).