• The quadratic equation whose roots are 3 and -1, is

    A) \( \Large x^{2}-4x+3=0 \)

      B) \( \Large x^{2}-2x-3=0 \)

    C) \( \Large x^{2}+2x-3=0 \)

      D) \( \Large x^{2}+4x+3=0 \)

    Correct Answer:
      B) \( \Large x^{2}-2x-3=0 \)

    Description for Correct answer

    Given that, the roots of the quadratic equation are 3 and -1.

    Let \( \Large \alpha = 3 \  and \  \beta = -1 \)

    Sum of roots = \( \Large \alpha + \beta = 3 - 1 = 2 \)

    Product of roots = \( \Large \alpha . \beta = \left(3\right) \left(-1\right) = -3 \)

    Therefore, Required quadratic equation is

    \( \Large x^{2} - \left( \alpha + \beta \right) x + \alpha \beta = 0 \)

    \( \Large x^{2} - \left(2\right)x + \left(-3\right) = 0 \)

    \( \Large x^{2} - 2x - 3 = 0 \)


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