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Write whether the following statements a...

Write whether the following statements are true or false. Justify your answers.
(i) Every quadratic equation has exactly one root.
(ii) Every quadratic equation has atleast one real root.
(ii) Every quadratic equation has atleast two roots.
(iv) Every quadratic equations atmost two roots.
(v) If he coefficient of `x^(2)` and the constnat term of a quadratic equation have opposite sigh, then the quadratic equation has real roots.
(vi) If the coefficient of `x^(2)` and the constant term have the same sign and if the coefficient of `x` term is zero, then the quadratic equation has no real roots.

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Knowledge Check

  • If the roots of a quadratic equation are -1 and 3, then the quadratic equation is

    A
    `x^2-2x-3=0`
    B
    `x^2+2x-3=0`
    C
    `x^2-2x+3=0`
    D
    `x^2+2x+3=0`

  • Every Quadratic Equation can have at most

    A
    Three roots
    B
    One root
    C
    Two roots
    D
    Any number of roots

  • A quadratic equation has double root, then

    A
    the two roots lie on the different sides of the axis
    B
    the quadratic equation cannot be expressed in the form of a perfect square.
    C
    the product of the roots is always negative.
    D
    the sum of the roots may be positive or negative.

    • Similar Questions

    Explore conceptually related problems

    Write whether the following statements are true or false. Justify your answers. Every quadratic equation has at most two roots.

    Write whether the following statements are true or false. Justify your answers. Every quadratic equation has at least two roots.

    If the coefficient of x^(2) and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots. State true or false and justify your answer.

    If one root of a quadratic equation is 2 + sqrt5 , then find the quadratic equation.

    Which of the followig quadratic equations has real roots ?

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