Important Questions For Board Exam:Polynomials

Important Questions, Revision Notes and Video Lectures on Real Numbers for Class 10 Board Exam (Padhte Chalo, Badhte Chalo- Eckovation). Join Group Code 101010 to discuss your doubts with educators from IIT Delhi

  • Unit 2 of class X CBSE contains 4 chapters which includes
    1.Polynomials
    2.Pair of linear equation in two variables
    3.Quadratic Equations
    4.Arithmetic Progression
  • This unit carries 20 marks out of 80
  • Click here to download revision notes of polynomials

Short Answer Type Questions

  1. If α and β are the zeros of the polynomial 2x ²– 7x + 3. Find the sum of the reciprocal of its zeros.
  2. If α& β are the zeros of the polynomial p(x) = x² – a (x + 1) – b such that (α+ 1) ( β+ 1) = 0 then find value of b.
  3. If α& β are the zeros of the polynomial x ²– (k + 6) x + 2 (2k – 1). Find k if α+β=1/2αβ
  4. If (x + p) is a factor of the polynomial 2x² + 2px + 5x + 10 find p.
  5.  Find a quadratic polynomial whose zeroes are  (5+ 3 √2) and (5- 3 √2) .
  6. If 1/5 and – 2 are respectively product and sum of the zeroes of a quadratic polynomial. Find the polynomial.
  7.  Find zeroes of  √ 3x²- 8x+ 4 √3.
  8. If (x + k) is a factor of the polynomial x ²–2x–15 and x ³+ a. Find k and a.
  9.  Form a quadratic polynomial, one of whose zero is (2+√5)  and the sum of zeros is 4.
  10. If sum of the zeroes of kx² + 3k + 2x is equal to their product. Find k.

Long Answers Type Questions

  1. Find the zeroes of 6x ² – 3 – 7x. Verify the relationship between the zeros and coefficients.
  2. If one zero of he polynomial (a² + a) x ² + 13x + 6a is reciprocal of the other, find value (s) of a.
  3. –5 is one of the zeroes of 2x ² + px – 15. Quadratic polynomial p(x ²+ x) + k has both the zeros equal to each other. Then find k.
  4.  Find the value of k such that 3x² + 2kx + x – k – 5 has the sum of the zeros as half of their product.
  5.  If (x – 2) is one of the factors of x ³– 3x ² – 4x + 12 find the other zeros.
  6.  If α& β are the zeros of he polynomial x ²– 5x + k such that α-β= 1, find the value of k.
  7.  If α& β are zeros of quadratic polynomial 2x² + 5x + k, find the value of k, such that (α+ β)²-αβ = 24.
  8. . What does the graph of the polynomial ax²+ bx + c represents. What type of graph will it represent (i) for a > 0, (ii) for a < 0. What happens if a = 0.
  9. If one zero of 4x² – 9 – 8kx is negative of the other find k

Answers

Short Answer Type Question

1  1/α+1/β  =7/3                         2  1                                     3  k=7                               4 p=2                       5 x²– 10x + 7

6 x²+2x+1/5                            7 2√3,2/3√3                   8 k = – 5, 3 and a = –125 + 27                    9 x ² – 4x – 1                      10  -2/3

Long Answer Type Questions

1 .1 /3 , 3 /2                                    2 5                                     3 p=7, k=7/4                  4 k=1                             5–2, 3

6 k = 6                                               7 k = 2                              8  A curve (parabola) upward parabola, downward parabola, straight line.

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