If roots of the quadratic equation px2-2√ 5 px+15 = 0 are real, then find the value of p.

Question

If roots of the quadratic equation px2-2√ 5 px+15 = 0 are real, then find the value of p.

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Mia 1 week 2022-01-15T09:01:20+00:00 1 Answer 0 views 0

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    2022-01-15T09:02:40+00:00

    Answer:

    For real roots, discriminant must be greater than 0 or equal to 0.

    Discriminant, for ax^2 + bx + c = 0, is given by b^2 – 4ac.

    Here, b = -2

    \sqrt5 p

    c = 15

    a = p

    = > discrimiant > 0

    = > (-2\sqrt5 )^2 – 4(15)p > 0

    = > 20 – 60p > 0

    = > 1/3 > p

    Solution set for the values of p is { …0,1/9…1/4} or accurately, (-infinity,1/3 ).

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