Important Questions :Quadratic Equations

Important Questions, Revision Notes and Video Lectures on Quadratic Equations 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 Quadratic Equation

  1. . If one root of the equation x² + 7x + k = 0 is –2, then find the value of k and the other root.
  2.  For what value of ‘k’ the equation 2x ² + kx + 3 = 0 has equal roots?
  3.  For what value of ‘p’, the equation 3x²+ px + 3 = 0 has real roots?
  4.  The product of two consecutive odd integers is 63. Represent this in form of a quadratic equation.
  5.  Divide 51 in to two parts such that their product is 378.
  6.  Find ‘k’ so that (k – 12) x 2 + 2 (k – 12) x + 2 = 0 has equal roots. (k  12). 24. If (–5) is a root of the equation 2x 2 + px – 15 = 0 and the equation p(x 2 + x) + k = 0 has equal roots, find values of p and k.
  7. A two digit number is such that the product of the digit is 35, when 18is added to the number, the digits inter change their places. Find the number.
  8. Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46, find the integers.
  9.  A motor boat whose speed is 9 km/h in still water goes 12 km down stream and comes back in a total time 3 hours. Find the speed of the stream.
  10.  A train travels 360 km at uniform speed. If the speed had been 5 km/hr more it would have taken 1 hour less for the same journey. Find the speed of the train.
  11.  The hypotenuse of right angled triangle is 6cm more than twice the shortest side. If the third side is 2 cm less than the hypotenuse, find the sides of the triangle.
  12.  By a reduction of Rs. 2 per kg in the price of sugar. Anita can purchase 2 kg sugar more for Rs. 224. Find the original price of sugar per kg.
  13. Rs. 6500 were divided equally among a certain number of students. Had there been 15 more students, each would have got Rs. 30 less. Find the original number of students.
  14.  A fast train takes 3 hours less than a slow train in travelling 600 km. If the speed of fast train is 10 km/kr more than the speed of slow train, find the speed of both the trains.
  15.  A girl is twice as old as her sister. Four years hence, the product of their ages will be 160. Find their present ages.
  16.  Two years ago a man’s age was three times the square of his son’s age. Three years hence his age will be four times his son’s age. Find their present ages.
  17.  In a cricket match against Sri Lanka, Sehwag took one wicket less than twice the number of wickets taken by Unmukt. If the product of the number of wickets taken by these two is 15, find the number of wickets taken by each. 4
  18. A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days. Find the time taken by B to finish the work alone.
  19. Two pipes running together can fill a cistern in 30/11 minutes. If one pipe takes 1 minute more than the other to fill the cistern, find the time in which each pipe would fill the cistern alone.
  20. If the roots of the equation (b – c)x 2 + (c – a) x + (a – b) = 0 are equal, then prove that 2b = a + c.

Answers

1.. k = 10, second root = – 5                                2 .±2 √ 6                      3. p ≥ 6 or p  ≤- 6                               4. x ²+ 2x – 63 = 0

5. 9, 42                                                                              6. k = 14                     7.57                                                           8. 4, 5, 6

9. 3 km/hr.                                                                     10. 40 km/hr.           11. 26 cm, 24 cm, 10 cm               12. Rs. 16

13. 50                                                                               14. 40, 50.                  15. 12, 6                                                16 27 yrs., 5 yrs.

17 30 days                                                                   19. 5, 6 min                20. Hint : For equal roots D = 0

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