ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Quadratic Equations
Question 1
1.
    • The sum of the roots of the quadratic equation
    • (
      36
      x
      2
       
      −
      12
      x
      +
      1
      		)
      =
      0
    • is
  • (
    -1
    3
    		 )
  • 1
  • 1
    5
  • 1
    3
Question 2
2.
    • If
    • p
    • and
    • q
    • are the roots of
    • (
      x
      2
       
      −
      9
      x
      +
      14
      		)
      =
      0
    • ,
    • find the equation whose roots are
    •  
       
      p
      		  +  
       
       
      1
       
       
      q
    • and
    •  
       
      q
      		  +  
       
       
      1
       
       
      p
  • (
    28
    x
    2
     
    −
    263
    x
    +
    435
    		)
    =
    0
  • (
    14
    x
    2
     
    −
    135
    x
    +
    225
    		)
    =
    0
  • (
    14
    x
    2
     
    −
    149
    x
    +
    255
    		)
    =
    0
  • (
    14
    x
    2
     
    −
    131
    x
    +
    195
    		)
    =
    0
  • (
    10
    x
    2
     
    −
    97
    x
    +
    165
    		)
    =
    0
Question 3
3.
    • Find the roots of the quadratic equation
    • (
      x
      2
       
      +
      9
      x
      +
      8
      		)
      =
      0
  • (
    0
    ,
    -9
    )
  • (
    1
    ,
    -9
    )
  • (
    0
    ,
    -8
    )
  • (
    1
    ,
    -11
    )
  • (
    -1
    ,
    -8
    )
Question 4
4.
    • Solve :
    •  
       
      3

      √

      3
      x
      2
       
      		  +  
       
       
      21
      x
      		  −  
       
       
      8

      √

      3
      		 = 
      0

  • √

    12
    3
    ,
    (
    −
    8

    √

    4
    )

    √

    3

  • √

    3
    3
    ,
    (
    −
    8
    )

    √

    3

  • √

    12
    3
    ,
    (
    −
    8
    )

    √

    3

  • √

    3
    3

    √

    4
    ,
    (
    −
    8
    )

    √

    12

  • √

    3
    3
    ,
    (
    −
    8
    )

    √

    12
Question 5
5.
    • Find the quadratic equation with roots
    • (
      -5
      ,
      -5
      )
  • (
    x
    2
     
    +
    12
    x
    +
    35
    		)
    =
    0
  • (
    x
    2
     
    +
    10
    x
    +
    25
    		)
    =
    0
  • (
    x
    2
     
    +
    8
    x
    +
    15
    		)
    =
    0
  • (
    x
    2
     
    +
    11
    x
    +
    30
    		)
    =
    0
  • (
    x
    2
     
    +
    9
    x
    +
    20
    		)
    =
    0
Question 6
6.
    • The sum of the roots of the quadratic equation
    • (
      6
      x
      2
       
      −
      11
      x
      −
      72
      		)
      =
      0
    • is
  • 13
    8
  • 9
    4
  • 11
    6
  • 13
    6
  • 3
    2
Question 7
7.
    • Solve :
    •  
       
      27
      x
      2
      a
      4
      b
      2
      		  −  
       
       
      3
      x
      a
      2
      b
      		  −  
       
       
      4
    • = 0
  •  
     
    4
     
     
    7
    a
    2
    b
    ,
    −
     
     
    1
     
     
    a
    2
    b
  •  
     
    4
     
     
    11
    a
    2
    b
    ,
    −
     
     
    1
     
     
    5
    a
    2
    b
  •  
     
    2
     
     
    3
    a
    2
    b
    ,
     
     
    1
     
     
    3
    a
    2
    b
  •  
     
    4
     
     
    9
    a
    2
    b
    ,
    −
     
     
    1
     
     
    3
    a
    2
    b
  •  
     
    2
     
     
    9
    a
    2
    b
    ,
    −
     
     
    1
     
     
    a
    2
    b
Question 8
8.
    • Find the discriminant of the quadratic equation
    • (
      x
      2
       
      −
      2
      x
      +
      1
      		)
      =
      0
  • 2
  • -2
  • -1
  • 1
  • 0
Question 9
9.
    • The sum of the roots of the quadratic equation
    • (
      x
      2
       
      +
      4
      x
      +
      4
      		)
      =
      0
    • is
  • -5
  • -1
  • -3
  • -4
  • -6
Question 10
10.
    • Find the roots of the quadratic equation
    • (
      12
      x
      2
       
      −
      28
      x
      +
      8
      		)
      =
      0
  • (
    3
    ,
    1
    3
    )
  • (
    4
    ,
    1
    )
  • (
    3
    ,
    1
    )
  • (
    2
    ,
    1
    3
    )
  • (
    4
    ,
    (
    -1
    3
    		 )
    )