Class 10 Math Chapter 2 Important Question

Class 10^th Maths
Sample Paper for Polynomials

1.  For what value of k, (–4) is a zero of the polynomial x² – x – (2k + 2)?

(CBSE 2009)

2.  For what value of p, (–4) is a zero of the polynomial x² – 2x – (7p + 3)?

(CBSE 2009)

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

(Al CBSE 2009)

4.  If (x + a) is a factor of 2x² + 2ax + 5x + 10 find a.

(Al CBSE 2008 F)

5.  Write the zeroes of the polynomial x² + 2x + 1.

(CBSE 2008)

6.  Write the zeroes of the polynomial x² – x – 6.

(CBSE 2008)

7.  Write a quadratic polynomial, the sum and product of whose zeroes are 3 and –2 respectively.

(CBSE 2008)

8.  Write the number of zeroes of the polynomial y = f(x) whose graph is given in the figure.

(Al CBSE 2008)

9.  The graph of y = f(x) is given in figure. How many zeroes are there of f(x)?

(Al CBSE 2008 C)

10.  The graph of y = f(x) is given in the figure. What is the number of zeroes of f(x)?

(CBSE 2008 C)

11.  What is the number of zeroes of the polynomial y = p(x)?

(AI CBSE 2010)

12.  Find the zeroes of the quadratic polynomial 6x² – 3 – 7x and verify the relationship between the zeroes and the coefficient of the polynomial.

(CBSE 2008)

13.  Find the zeroes of the quadratic polynomial 5x² – 4 – 8x and verify the relationship between the zeroes and the coefficient of the polynomial.

(AI CBSE 2008)

14.  Find the quadratic polynomial, the sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.

(CBSE 2008)

15.  If one zero of the polynomial (a² – 9) x² + 13x + 6a is reciprocal of the other, find the value of ‘a’.

(AI CBSE 2008)

16.  If the product of zeroes of the polynomial ax² – 6x – 6 is 4, find the value of ‘a’.

(AI CBSE 2008)

17.  Find all the zeros of the polynomial x⁴ + x³ – 34x² – 4x + 120, if two of its zeroes are 2 and – 2.

(AI CBSE 2008)

18.  Find all the zeroes of the polynomial 2x⁴ + 7x – 19x² – 14x + 30, if two of its zeroes are 

(AI CBSE 2008)

19.  Find the quadratic polynomial whose zeroes are 1 and –3. Verify the relation between the coefficients and the zeroes of the polynomial.

(CBSE 2008 C)

20.  Find the zeroes of the quadratic polynomial 4x² – 4x – 3 and verify the relation between the zeroes and its coefficients.

(CBSE 2008 C)

21.  Obtain all other zeroes of the polynomial 2x³ – 4x – x² + 2, if two of its zeroes are 

(CBSE 2008 C)

22.  Find all the zeroes of x4 – 3x³ + 6x – 4, if two of its zeroes are 

(AI CBSE 2008 C)

23.  Find a quadratic polynomial whose zeroes are –4 and 3 and verify the relationship between the zeroes and the coefficients.

(AI CBSE 2008 C)

24.  Using division algorithm, find the quotient and remainder on dividing f(x) by g(x), where f(x) = 6x³ + 13x² + x – 2 and g(x) = 2x + 1

(AI CBSE 2008 C)

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

(CBSE 2009)

26.  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.

(CBSE 2009)

27.  Find all the zeroes of the polynomial x³ + 3x² – 2x – 6, if two of its zeroes are – 

(AI CBSE 2009)

28.  Find all the zeroes of the polynomial 2x³ + x² – 6x – 3, if two of its zeroes are – 

(AI CBSE 2009)

29.  If α and β are zeroes of the quadratic polynomial x² – 6x + a; find the value of ‘a’ if 3α + 2β = 20.