• Find the roots of the equation \( \Large 2x^{2}-11x+15=0 \)

    A) \( \Large 3 \ and \ \frac{5}{2} \)

      B) \( \Large -3 \ and \ -\frac{5}{2} \)

    C) \( \Large 5 \ and \ \frac{3}{2} \)

      D) \( \Large -5 \ and \ -\frac{3}{2} \)

    Correct Answer:
    A) \( \Large 3 \ and \ \frac{5}{2} \)

    Description for Correct answer

    \( \Large 2x^{2} - \left(6x + 5x\right) + 15 = 0 \)

    [by factorization method]

    = \( \Large 2x^{2} - 6x - 5x + 15 = 0 \)

    = \( \Large 2x \left(x - 3\right) - 5 \left(x - 3\right) = 0 \)

    = \( \Large \left(2x - 5\right) \left(x - 3\right) = 0 \)

    Therefore, \( \Large x = \frac{5}{2}, 3 \)

    Hence, the roots are \( \Large \frac{5}{2}, 3 \)


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