mx²-2x+p=0 have equal roots find the value of m and p

Question

mx²-2x+p=0 have equal roots find the value of m
and p

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Amelia 2 months 2021-10-10T12:54:02+00:00 1 Answer 0 views 0

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    2021-10-10T12:55:55+00:00

    Answer:

    The value of m = 1/p

    The value of p = 1/m

    Step-by-step explanation:

    f(x) = mx² – 2x + p = 0 has equal roots.

    Then the discriminant b² – 4ac = 0

    Therefore b²- 4ac = (-2)² – 4mp = 0

    => 4 – 4mp = 0

    or 4mp = 4

    => mp = 1

    Which implies that, ‘m’ is the reciprocal of p

    or m = 1/p

    Roots of the equation = (-b + or – √b² – 4ac) ÷ 2a

    = (-(-2) + or – 0) ÷ 2m

    = 2/2m => 1/m

    Roots of the equation are [1/m , 1/m] or [p, p]

    Therefore, the value of m = 1/p

    & the value of p = 1/m

    The equation can have any values, but, value of p must be the reciprocal of m and vice versa.

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