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

## Answers ( )

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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