Question

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

Answer 1

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

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Answer 2

Answer:

I think this may help you

Step-by-step explanation:

This question is a multiple choice question, so in this question answer will be as 2 answers.