Quadratic Equation


  1. The expression x2 − x + 1 has :









  1. View Hint View Answer Discuss in Forum

    According to question , we have
    Comparing x2 - x + 1 with ax2 + bx + c , we get
    a = 1, b = −1, c = 1
    Here D = b2 - 4ac = ( - 1 )2 - 4 (1)(1)
    = 1 - 4 = - 3

    Correct Option: C

    According to question , we have
    Comparing x2 - x + 1 with ax2 + bx + c , we get
    a = 1, b = −1, c = 1
    Here D = b2 - 4ac = ( - 1 )2 - 4 (1)(1)
    = 1 - 4 = - 3
    Since D < 0, so the given expression has no proper linear factor.


  1. The length of a rectangular plot is 8 m greater than its breadth. If the area of the plot is 308 m2, find the length of the plot.









  1. View Hint View Answer Discuss in Forum

    Let, the breadth of the rectangular plot be x m. Then the length of rectangular plot = (x + 8) m
    ∴ Area = Length × Breadth = x(x + 8)m2 But the area of the plot is given to be 308 m2
    ∴ x( x + 8 ) = 308 ⇒ x2 + 8x - 308 = 0

    Correct Option: C

    Let, the breadth of the rectangular plot be x m. Then the length of rectangular plot = (x + 8) m
    ∴ Area = Length × Breadth = x(x + 8)m2 But the area of the plot is given to be 308 m2
    ∴ x( x + 8 ) = 308 ⇒ x2 + 8x - 308 = 0
    ⇒ x2 + 22x - 14x - 308 = 0
    ⇒ x( x + 22 ) - 14 ( x - 22 ) = 0
    ⇒ ( x + 22 ) ( x - 14 ) = 0
    ⇒ x = 14, -22
    But, x = −22 is not possible, since breath cannot be negative
    ∴ x = 14
    Hence the breadth of the rectangular plot = 14 m Length of the rectangular plot = (14 + 8) m = 22 m.



  1. The value of x in the equation
    x +
    1
    2 -
    3
    x -
    1
    = 4 is :
    x2x









  1. View Hint View Answer Discuss in Forum

    We can say that ,

    Putting in above equation , x -
    1
    = y
    x

    x +
    1
    2= x2 +
    1
    + 2 =x +
    1
    2+ 4 = y2 + 4
    xx2x

    Correct Option: C

    We can say that ,

    Putting in above equation , x -
    1
    = y
    x
    x +
    1
    2= x2 +
    1
    + 2 =x +
    1
    2+ 4 = y2 + 4
    xx2x
    So, given equation becomes
    ⇒ yy -
    3
    = 0 ⇒ y = 0 or y =
    3
    22

    ∴ x -
    1
    = 0 ⇒ x -
    1
    =
    3
    x
    x
    2

    ⇒ x2 - 1 = 0 or 2x2 - 3x - 2 = 0
    ⇒ x = ± 1 or ( 2x + 1 ) ( x - 2 ) = 0
    ⇒ x = ± 1 or - 1/2 or x = 2.
    Thus , option C is correct answer .