Quadratic Equations

  • Question 1
    CBSEENMA10006442

    Check whether the following are quadratic equations:
    (x + 1)2 = 2(x – 3)

    Solution

    L.H.S. = (x + 1)= x2 + 2x + 1
    R.H.S. = 2(x – 3) = 2x –6
    ∴ 6x2 + 2x + 1 = 2x - 6
    ⇒ x2 + 2x + 1–2x + 6 = 0
    ⇒ x2+ 7 = 0
    ∵ It is of the form ax2 + bx + c = 0, where a = 1,b = 0, c = 7.
    Hence, the given equation is a quadratic equation.

    Question 2
    CBSEENMA10006443

    Check whether the following are quadratic equations:
    x– 2x = (–2) (3 – x)

    Solution

    R.H.S. = (–2) (3 – x) = – 6 + 2x
    ∴ x2 – 2x = – 6 + 2x
    ⇒ x2 – 2x + 6 – 2x = 0
    ⇒ x2 – 4x + 6 = 0
    ∵ It is of the form ax2 + bx + c = 0 where a = 1,b = –4, c = 6.
    Hence, the given equation is a quadratic equation.

    Question 3
    CBSEENMA10006444

    Check whether the following are quadratic equations:
    (x – 2) (x + 1) = (x – 1) (x + 3)

    Solution

    L.H.S. = (x–2) (x + 1)
    = x2 – x – 2
    R.H.S. = (x – 1) (x + 3)
    = x2 + 2x – 3
    ∴ x2 – x – 2 = x2 + 2x – 3
    ⇒ – x –2 – 2x + 3 = 0
    ⇒ – 3x + 1 = 0
    ∵ It is not of the form ax2 + bx + c = 0.
    Hence, the given equation is not a quadratic equation. 

    Question 4
    CBSEENMA10006445

    Check whether the following are quadratic equations:
    (x – 3) (2x + 1) = x(x + 5)

    Solution

    L.H.S. = (x – 1) (2x + 1)
    = 2x2 + x – 2x – 1
    = 2x2 – x – 1
    R.H.S. = x(x + 5) = x2 + 5x
    ∴ 2x2 – x – 1 = x2 + 5x
    ⇒ 2x2 – x2 – x – 5x – 1 = 0
    ⇒ x2 – 6x – 1 = 0
    ∵ It is of the form ax2 + bx + c = 0 where a = 1, b = –b, c = –1.
    Hence, the given equation is a quadratic equation.

    Sponsor Area

    Mock Test Series

    Sponsor Area

    NCERT Book Store

    NCERT Sample Papers

    Entrance Exams Preparation