If x^2+2(m+2)x+9m=0 have equal roots then find m​

Question

If x^2+2(m+2)x+9m=0 have equal roots then find m​

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Isabelle 2 months 2021-11-10T22:33:33+00:00 1 Answer 0 views 0

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    2021-11-10T22:35:17+00:00

    Method 1 :

    x^2 + 2(m+2)x + 8m + m=0
    x^2 + 2mx +4x + 8m + m = 0
    x(x+2m) + 4(x+2m) + m = 0
    (x + 4)(x + 2m) = -m

    x + 4 = -m
    -x -4 = m

    x + 2m = -m
    -x/3 = m

    Method 2 : this one is the correct method

    If the above equation has equal roots then D = b2 – 4ac = 0
    x^2 + 2(m + 2)x + 9m = 0
    [a=1 b=2(m+2) c=9m]

    D = b2 – 4ac = 0
    D = [2(m+2)]^2 – 4(1)(9m) = 0
    D = 4(m2 + 4m + 4) – 36m = 0
    D = 4m^2 + 16m + 16 – 36m = 0
    D = 4m^2 – 20m +16 =0
    4(m^2 – 5m + 4) = 0
    (m^2 – 4m -m + 4) =0
    m(m -4) -1(m-4) =0
    (m-1)(m-4) = 0

    m-1 = 0 =>
    m=1

    m-4 = 0 =>
    m=4

    hope it helps please mark as brainliest

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