CBSE Class 10 Mathematics Quadratic Equation Worksheet Set E

QUADRATIC EQUATIONS

∴ The required two digit number = 10x + y

= 10 × 5 + 7 = 57 

More question-

 SECTION A: (1 MARK)

1. Find the value of  (-2,3)

2.A polygon of n sides has diagonals. How many sides has a polygon with 54 diagonals? (12)

3. Find the roots of the equation ax² + a = a²x + x (a, )

SECTION B: (2 MARKS)

4. Solve for x : (CBSE BOARD 2012) (-4,)

5. Find the value of p for which x2 + 5px + 16 = 0 has no real roots. ()

6.One day, I asked the son of my close friend about his age. The child replied in a different way. He said, “One year ago, my dad was 8 times as old as me and now his age is equal to square of my age.” Represent this situation in the form of a quadratic equation. (CBSE BOARD 2007) (x²-8x+7=0)

7. Find the value of p for which the quadratic equation 4x2 – 3px + 9 = 0 has real roots. ( p )

8. If y =1 is a common root of the equations ay2 + ay + 3 = 0 and y2 + y + b = 0, find ab. (CBSE BOARD 2012) ( 3 )

SECTION C: (3 MARKS)

9. Solve for x : 2 2x + 3 = 65(2x – 2) + 122 (CBSE BOARD 2012) (-3,3)

10. Solve for x : x2 + 5x – (a2 + a – 6) = 0. [-(a+3),(a-2)]

11. Solve for x: 9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0.

12. Solve for x: , x (CBSE BOARD 2004) [ (a+b), ]

13. Solve for x : (x (CBSE BOARD 2005) ( -a , -b)

14. Solve for x: + = (x ≠ 0,1) (CBSE BOARD 2000) ( )

SECTION D: (4 MARKS)

15. The numerator of a fraction is 1 less than the denominator. If 3 is added to each of the numerator and denominator, the fraction is increased by 3/28. Find the fraction. (CBSE BOARD 2016) (3/4)

16. The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples. (CBSE BOARD 2016) (14,21)

17. The total cost of a certain length of a piece of cloth is ₹200. If the piece was 5m longer and each meter of cloth costs ₹2 less, the cost of the piece would have remained unchanged. How long is the piece and what is its original rate per meter? (CBSE BOARD 2012) (20m,₹10)

18. If the roots of the quadratic equation x² + 2px + mn = 0 are real and equal, show that the roots of the quadratic equation x2 – 2(m + n)x + (m² + n² + 2p²) = 0 are also equal. (CBSE BOARD 2008)

19. A tank can be filled by one pipe in x minutes and emptied by another pipe in (x + 5) minutes. Both the pipes when opened together can fill the empty tank in 16.8 minutes. Find x. (EXEMPLAR PROBLEM) (7 hours)

20. Solve for x: 5 x + 1 + 5 2 – x = 126 (2,-1)

21. If the roots of the equation (a – b) x² + (b – c) x + (c – a) = 0 are equal, prove that 2a = b + c. (EXEMPLAR PROBLEM)

22. Solve for x : (-1)

23. Students of class X collected ₹18000. They wanted to divide it equally among a certain number of students residing in slum area. When they started distributing the amount, 20 more students from the nearby slums also joined. Now each student get ₹240 less. (a) Find the number of students living in the slum. (b) Which value is depicted by the students? (CBSE BOARD 2013) (30)

24. Out of a number of saras birds , one fourth of the number are moving about in lots, 1/9 th coupled with ¼ th as well as 7 times the square root of the number move on a hill, 56 birds in vakula trees. What is the total number of birds? (CBSE BOARD 2004) (576)

25. At t minutes past 2 p.m. the time needed by the minutes hand of a clock to show 3 p.m. was found to be 3 minutes less than t2/4 minutes. Find t.

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