amath

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The roots of the quadratic equation x^2-mx+n=0 ,where m and n are integers ,are a and 1/4a.
(i)Find the sum and product of its roots
(ii)show that 4m^2=25n

How to do part 2 ?

  • amath -

    You must be studying the property of the roots of a quadratic, where
    sum of roots = -b/a
    product of roots = c/a

    so for x^2 - mx + n
    the sum of the roots = m
    product of the roots = n

    but you are given the roots as a and 1/4a
    sum of roots = a + 1/4a = (5/4)a
    product of roots = (1/4)a^2

    so (5/4)a = m --- >a = 4m/5 or a2 = 16m^2/25
    (1/4)a^2 = n --- a^2 = 4n

    thus: 16m^2/25 = 4n
    16m^2 = 100n
    4m^2 = 25n

    Voila!!!!

  • amath -

    ohh I get it !! thanks a lot :))

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