• If one of the roots of quadratic equation \( \Large 7x^{2}-50x+k=0 \) is 7, then what is the value of k?

    A) 7

      B) 1

    C) \( \Large \frac{50}{7} \)

      D) \( \Large \frac{7}{50} \)

    Correct Answer:
    A) 7

    Description for Correct answer

    Given equation is \( \Large 7x^{2}-50x+k=0 \)

    Here, a = 7, b = -50, c = k

    Since, \( \Large \alpha + \beta =\frac{-b}{a} \)

    Therefore, \( \Large \alpha + \beta =\frac{50}{7} \)

    or \( \Large \beta =\frac{50}{7}-7 \)

    => \( \Large \beta =\frac{1}{7} \) [Because \( \Large \alpha = 7 \)(given)]

    and \( \Large \alpha \beta =\frac{c}{a} \)

    or \( \Large 7 \times \frac{1}{7}=\frac{k}{7} \)

    k = 7


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