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]
