WORKSHEET OF QUADRATIC EQUATION CLASS-10

        WORKSHEET OF QUADRATIC EQUATION CLASS-10              

   

BASIC/STANDARD]

I. MULTIPLE CHOICE QUESTIONS

1. Which one of the following is not a quadratic equation ?

(a) (x + 2)² = 2(x + 3) 

(b) x² + 3x = (–1)(1 – 3x)²

(c) (x + 2)(x – 1) = x² – 2x – 3 

(d) x³ – x² + 2x + 1 = (x + 1)³

2. Which constant should be added and subtracted to solve the quadratic equation 4x² -√3x - 5= 0 ,by the method of completing the square ?

(a) 9/16

(b) 3/16 

(c) 3/4

(d) √3/4

3. Which of the following is a quadratic equation?

(a)x² + 2x + 1 = (4 – x)² + 3 

(b) –2x² = (5 – x) (2x - 2/5)

(c)(k + 1)x² + 3/2 x= 7, k= -1

(d) x³ – x² = (x – 1)³

4. Which of the following is not a quadratic equation?

(a) 2(x – 1)² = 4x² – 2x + 1 

(b) 2x – x² = x² + 5

(c) {√2x + √3}² + x² = 3 x² - 5x

(d) (x² + 2x)² = x⁴ + 3 + 4x³

5. Which of the following has 2 as a root ?

(a) x² – 4x – 5 = 0 

(b) x² + 3x – 12 = 0

(c) 2x² – 7x + 6 = 0 

(d) 3x² – 6x – 2 = 0

6. If 1/ 2 is a root of the equation x² + kx - 5/4, then the value of k is:

(a) 2 

(b) –2 

(c) 1/4

(d) 1/ 2

7. Which of the following equations has the sum of its roots as 3?

(a) 2x² – 3x + 6 = 0 

(b) –x² + 3x – 3 = 0

(c) √2 x² - 3/√2 x +1= 0

(d) 3x² – 3x + 3 = 0

8. Value of k for which the quadratic equation 2x² – kx + k = 0, has equal roots is:

(a) 1 

(b) 2 

(c) 5 

(d) 0, 8

9. Which constant must be added and subtracted to solve the quadratic equation  9 x² + 3 /4 x  -√2 = 0 , by the method of completing the square?

(a) 1/8

(b) 1/64 

(c) 1/4 

(d) 9/64

10. The quadratic equation 2 x² - √5 x + 1 = 0 has : 

(a) Two distinct real roots 

(b) Two equal real roots

(c) No real roots 

(d) More than 2 real roots

11. Which of the following equations has two distinct real roots ?

(a) 2x² – 3 √2 x + 9/4 = 0

(b) x² + x – 5 = 0

(c) x² + 3x + 2√ 2 = 0 

(d) 5x² – 3x + 1 = 0

12. Which of the following equations has no real roots?

(a) x² – 4x + 3 √2 = 0 

(b) x² + 4x – 3 √2 = 0

(c) x² – 4x – 3 √2 = 0 

(d) 3x² + 4 √3 x + 4 = 0

13. (x² + 1)² – x² = 0 has : 

(a) Four real roots 

(b) Two real roots

(c) No real roots 

(d) One real root

14. If 8 is a root of the equation x² – 10x + k = 0, then the value of k is:

(a) 2 

(b) 8 

(c) –8 

(d) 16

15. The quadratic equation whose roots are real and equal is:

(a) 2x² – 4x + 3 = 0 

(b) x² – 4x + 4 = 0

(c) 3x² – 5x + 2 = 0 

(d) x² – 2√ 2 x – 6 = 0

16. If a, b are the roots of the equation x² – 5x + k = 0, then what is the value of k such 

that a – b = 1 ?

(a) 1 

(b) 3 

(c) 4 

(d) 6

17. The roots of the equation x² – 3x – m(m + 3) = 0, where m is a constant, are :

(a) m, m + 3 

(b) –m, m + 3 

(c) m, –(m + 3) 

(d) –m, – (m + 3)

18. The roots of the equation x² + 3x – (m + 2)(m + 5) = 0, where m is a constant, are :

(a) (m + 2), (m +5) 

(b) (m + 2), – (m +5)

(c) – (m + 2), (m +5) 

(d) – (m + 2), – (m +5)

19. The roots of the equation x² + x – p(p + 1) = 0, where p is a constant, are : 

(a) p, p + 1 

(b) –p, p + 1 

(c) p, – (p + 1) 

(d) –p, – (p + 1)

20. If one root of the equation 5x² – 13x + k = 0, is reciprocal of the other, then k = 

(a) 0 

(b) 5 

(c) 6 

(d) 1/6

21. If one root of the equation 2x² – 10x + p = 0 is 2, then the value of p is :

(a) –3 

(b) –6 

(c) 9 

(d) 12

22. The root of the quadratic equation 2x² – x – 6 = 0 are :

(a) –2, 3/2 

(b) 2, – 3/2 

(c) –2, –3/2 

(d) 2, 3/2

23. The roots of the quadratic equation x² + 5x – (a + 1) (a + 6) = 0, where a is a constant 

are : 

(a) a + 1, a + 6 

(b) (a + 1), – (a + 6)

(c) –(a + 1), (a + 6) 

(d) –(a + 1), – (a + 6)

24. Roots of the quadratic equation 3x² – 5x + 2 = 0, are :

(a) 1, 3/2 

(b) 2/3, 1 

(c) 1/3, 5 

(d) –3/2, 1

25. Roots of the quadratic equation 3x² – 2 √6 x + 2 = 0 are

(a) ✓2/3 ,✓2/3

(b)  - ✓2/3 ,✓2/3

(c).  - ✓2/3 ,  - ✓2/3

(d). - ✓2/3 ,✓3/2

26. If (16 /x)  - 1  = 15 / x+1

, where x ≠ 0, –1, then x =

(a) ± 2 

(b) ± 3 

(c) ± 4 

(d) ± 6

27. If 3 / (x+1) -  1/2 = 2/(3x-1)

where x ≠ –1, 1/3

, then x =

(a) 1, 2 

(b) 1, 3 

(c) 2, 3 

(d) 3, 5

28. If (4/ x ) - 3 = 5/(2x+5)

  where x ≠ 0, –3/2 , then x =

(a) 1, 2 

(b) –1, –2 

(c) 1, –2 

(d) 2, –3

29. If 14 /(x+3) -1 = 5/(x+1) , where x ≠ –3, –1, then x =

(a) 1, 3 

(b) 1, 2 

(c) 1, 5 

(d) 1, 4

30. If the sum of a number and its reciprocal is 10/3 , then, the number is :

(a) 2/3 

(b) 3 

(c) 4 

(d) 10

31. If the sum of the squares of two consecutive natural numbers is 421, then the numbers 

are:

(a) 14 and –15 

(b) 14 and 15 

(c) 13 and 15 

(d) –13 and –15

32. If  1 / (x-1) - 1/(x+5) = 6 / 7

where x ≠ 1, –5), then x =

(a) 2 and –6 

(b) 3 and 5 

(c) 5 and 4 

(d) 2 and 6

33. If 1/ (x − 2) + 2/(x – 1) = 6/x

 (where x ≠ 0,1, 2), then x =

(a) 3, 2/3 

(b) 5, 7/3 

(c) 3, 4/3 

(d) 7, 5/3

34. The sum of two numbers is 16 and sum of their reciprocals is 1/3. The number are:

(a) 13 and 3 

(b) 4 and 12 

(c) 11 and 5 

(d) 10 and 6

35. Two numbers differ by 4 and their product is 192. The numbers are:

(a) 12 and 16

 (b) 10 and 6 

(c) 20 and 24 

(d) 18 and 14

36. Sum of two numbers is 27 and their product is 182. The numbers are:

(a) 13 and 14 

(b) 15 and 12 

(c) 20 and 7 

(d) 22 and 5

37. The roots of the quadratic equation 2x² + ax – a,² = 0 are :

(a) – a, a/2 

(b) a, – a/2 

(c) a, a/2

(d) None of these

38. The values of  k  for which the quadratic equation 9x² – 3kx + k = 0 has equal roots is :

(a) 4 

(b) 0 

(c) 0 or 4 

(d) 1 or 4

39. The values of p for which the quadratic equation 4x² + px + 3 = 0 has equal roots is :

(a) ± 4 √3 

(b) ± 3 √2 

(c) ± 3√ 3 

(d) ± 5 √3

40. Roots of the quadratic equation √3 x² – 2√ 2 x –2 √3 = 0 are :

(a) −√ 2/√3 , √6 

(b) √3/√2 ,√6 

(c) √2/√3,− √6 

(d) √3/√2, − √6

41. A natural number, when increased by 12, equals 160 times its reciprocal. The number is:

(a) 8 

(b) 6 

(c) 4 

(d) 2

42. Roots of the equation ✓ (3x²-2) = 2x-1 are:

(a) 3, 1 

(b) 4, 1 

(c) 3, 2 

(d) 2, 3

43. Roots of the quadratic equation 1/3 x²-√11x +1= 0 are: 

(a) {3 √11 ± √87}/2 

(b) 3√12

(c) 5 √11

(d) √87/11

44. Roots of the quadratic equation 4x² – 4px + (p² – q²) = 0 are :

(a) {p ± q} /2

(b)  {p ± q} /3

(c) {q ± p} /5

(d) {p ± q} /8

45. Roots of the quadratic equation (2x – 3)² = 16 are :

(a) 7/2, -1/2

(b) 5/2 ,  -3/2 ,  

(c) 7/2 , 3/2

(d) 11/2 ,7/2

46. If the sum and product of two numbers are 24 and 128 respectively, then numbers are:

(a) 16 and 8 

(b) 18 and 6 

(c) 22 and 2 

(d) 14 and 10

47. The value of p for which one root of the quadratic equation px² – 14x + 8 = 0 is 6 times the other is :

(a) 5 

(b) 3 

(c) –3 

(d) 2

48. If x = 1 is a common root of the equations ax² + ax + 3 = 0 and x² + x + b = 0, then 

the value of a ÷ b =

(a) 3/4 

(b) 4/3 

(c) –3/4 

(d) – 4/3

49. If x – 4 = 12/x ,then the values of x are :

(a) –2, –6  

(b) 6, 2  

(c) 6, –2 

(d) – 6, 2

50. Roots of the equation (x – 1)² – 5(x – 1) – 6 = 0 are:

(a) (7, 0) 

(b) (6, 0) 

(c) (7, 6) 

(d) (6, –7)

                                                                                             

II. FILL IN THE BLANKS

1. If two number differ by 2 and their product is 360, the numbers are ________ and 

–––––––––.

2. The roots of the equation 2x² – x + 1/8 = 0 are _____________.

3. The roots of the equation 100x² – 20x + 1 = 0 are _____________.

4. The roots of the equation a²b²x² + b²x – a²x – 1 = 0 are _____________.

5. If 12 is divided into two parts such that their product is 32. Then two parts are 

_____________ and __________.

6. The attitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, then sum of other two sides is _____________.

7. The two consecutive odd natural numbers, the sum of whose squares is 202 _____________.

8. If –4 is a root of the quadratic equation x² + px – 4 = 0 and the quadratic equation

x² + px + k = 0 has equal roots, then the value of k = _____________.

9. If the equation (1 + m²) x² + 2 mcx + (c² – a²) = 0, then, a² (1 + m²) = ___________.

10. If I had walked 1 km per hour faster, I would have taken 10 minutes less to to walk 2 km. The rate of my walking is _____________.

11. The value(s) of p for which the quadratic equation 4x² – 3px + 9 = 0 has real root is 

_____________.

12. The sides of a right angled triangle are x – 1, x and x + 1. Then sides are __________  and ___________.

13. The roots of the quadratic eqaution x² + 3x – m (m + 3) = 0 where m is a constant are  _________ and _________.

14. A natural number is greater than twice its square root by 3. The number is ___________.

15. If the root of the equation m²x² + 2x (mc – 2a) + c² = 0 are equal, then c = _____________.

                                                                                             

III. VERY SHORT ANSWER QUESTIONS

1. Write the standard form of a quadratic equation.

2. If x = α is a solution of the quadratic equation A x² + Bx + C = 0, then A α² + Bα + C = 0. Is it true?

3. Find the roots of the quadratic equation (x + 2)² = 0.

4. What is the discriminant of a quadratic equation ax² + bx + c = 0?

5. Write the descriminant of 2x² – 7 = 0.

6. Write the condition for the quadratic equation ax² + bx + c = 0, to have real roots.

7. State the condition for the quadratic equation ax² + bx + c = 0 to have equal real roots.

8. State the condition for the quadratic equation ax³ + bx + c = 0 to have no real roots.

9. State Shreedharacharya Formula.

10. Find the nature of the roots of the quadratic equation 2x² – 4x + 3 = 0. [Cbse 2019]

11. For what values of k, the roots of the equation x² + 4x + k = 0 are real? [Cbse 2019]

12. If x = 3 is one root of the quadratic equation, x² – 2kx – 6 = 0, then find the value of k. [Cbse 2018]