CBSE Class 10 Mathematics Important Questions for Exam 2023 (Chapter - Polynomials)

 

These Mathematics Questions of Chapter {Polynomials} are important for CBSE Examination 2023. So all the candidates Revise and Practices all the questions carefully

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1)      If (x + k) is a factor of 2x² + 2kx + 5x + 10, find k.

2)      If α and β are the zeroes of the polynomial p(x) = 3x² – 5x + 6, find

a.      (i) (α / β) + (β / α)                               (ii) α³ + β³

3)      Find a polynomial whose zeros are squares of the zeroes of the polynomial 3x² + 6x – 9.

4)      If ‘1’ is one of the zeroes of the polynomial p(x) = 7x – x³ – 6 find its other zeroes.

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

6)      If the sum of the zeroes of the quadratic polynomial kx² + 2x + 3k is equal to their product, find k.

7)      Find the polynomial whose zeroes are reciprocals of the zeroes of the polynomial 2x² + 3x – 6.

8)      Find the ratio of the sum and product of the zeroes of the polynomial 5x² + 2x – 10.

9)      If α, β and γ are the zeroes of the cubic polynomial p(x) = 3x³ – 6x² + 5x – 3, then find their sum and product.

10)  Divide 3 – x + 2x² + x³ – 3x4 by (2 – x ) and verify by division algorithm.

11)  Find all the zeroes of the polynomial p(x) = x4 – 7x³ + 9x² + 13x – 4, if two of its zeroes are 2 + √ 3 and

2 - √ 3.

12)  What must be subtracted from 8x4 + 14x³ - 2x² + 7x – 8 so that the resulting polynomial is exactly divisible by 4x² + 3x – 2.

13)  Find all the zeroes of the polynomial f (x) = 2x4 – 3x³ – 5x² + 9x – 3, if two of its zeroes are ± √ 3.

14)  If α and β are the zeroes of the polynomial x² - 4√3x + 3, then find the value of α + β – αβ.

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

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16)  If the sum of the zeroes of a quadratic polynomial ky² + 2y – 3k is equal to twice their product, find the value of k.

17)  Find the zeroes of the quadratic polynomial √3x² – 8x + 4√3.

18)  Find the value of a and b, if they are the zeroes of polynomial x² + ax + b.

19)  If α and β are the zeroes of the polynomial x² – x – k, such that α – β = 9. Find k.

20)  Find the all the zeroes of x² – 2x.

21)  If p and q are the zeroes of polynomial 2x² – 7x + 3, find the value of p² + q²

22)  Find the value of k, if -1 is a zero of the polynomial kx² – 4x + k.

23)  If the zeroes of the polynomial x² +px + q are double in value to the zeroes of 2x² – 5x – 3, find the value of p and q.

24)  Form a quadratic polynomial p(x) with 3 and -2/5 as sum and product of its zeroes, respectively.

25)  If the sum of the zeroes of the polynomial P(x) = (a+1)x² + (2a + 3)x + (3a + 4) is -1, then find the product of zeroes.

26)  Find the quadratic polynomial whose zeroes are 3 + √2 and 3 - √2.

27)  Quadratic polynomial 2x² – 3x + 1 has zeroes as α and β. Now form a quadratic polynomial whose zeroes are 3α and 3β.

28)  Find the zeroes of the quadratic polynomial x² - 2√2x and verify the relationship between the zeroes and the coefficient.

29)  If zeroes of the polynomial x² + 4x + 2a are α and 2/α, then find the value of a.

30)  Verify whether 2, 3 and ½ are the zeroes of the polynomial p(x) = 2x³ – 11x² + 17x – 6.

31)  If one zero of a polynomial 3x² – 8x + (2k + 1) is seven times the other, find the value of k.

32)  If α and β are the zeroes of the polynomial x² – 6x + k then find the value of k such that α² + β² = 40.

33)  If α and β are the zeroes of the polynomial P(x) = 3x² – 4x – 7 then form quadratic polynomial whose zeroes are 1/α and 1/β.

34)  If α and β are the zeroes of the quadratic polynomial such that α + β = 24 and α – β = 8. Find the quadratic polynomial having α and β as its zeroes. Verify the relationship between the zeroes and coefficients of the polynomial.

35)  If the sum and product of the zeroes of the polynomial ax² – 5x + c is equal to 10 each, find the value of a and c.

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36)  If α and β are the zeroes of the polynomial x² – 2x – 8, then form a quadratic polynomial whose zeroes are 3α and 3β.

37)  If α and β are the zeroes of the polynomial x² – p(x + 1) + c such that (α + 1) (β + 1) = 0, then find the value of c.

38)  Polynomial x⁴ + 7x³ + 7x² + px + q  is exactly divisible by x² + 7x + 12 find the value of p and q.

39)  If α and β are the zeroes of the polynomial 2x² + 5 + k satisfying the relation α² + β² + αβ = 21/4, then find the value of k.

40)   Given that x - √5 is a factor of the polynomial x³ - 3√5x² – 5x + 15√5, find all the zeroes of the polynomial.

41)  Obtain all other zeroes of the polynomial 4x⁴ + x³ – 72x² – 18x, if two of its zeroes are 3√2 and -3√2.

42)  Obtain all other zeroes of the polynomial 9x⁴ - 6x³ – 35x² + 24x - 4, if two of its zeroes are 2 and -2.

43)  If α and β are the zeroes of the quadratic polynomial x² + x – 2 then find a polynomial whose zeroes are 2α + 1 and 2β + 1.

44)  If x³ + 8x² + kx + 18 is completely divisible by x² + 6x + 9 then find the value of k.

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

46)  If the polynomial 3x⁴ – 9x³ + x² + 15x + k is completely divisible by 3x² – 5 find the value of k and hence the other two zeroes of the polynomial.

      47) If the polynomial x⁴ – 6x³ + 16x² – 25x + 10 is divided by another polynomial x² – 2x + k,          the remainder comes out to be x + a then find the value of K and a.