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Question

The quadratic equation kx²+5mx+9k=0 has two equal rroots.Given that k and m are positive,find the positive ratio k:m and solve the equation.

Answer 1

when you have two equal roots the discriminant is equal to 0

b^2-4ac=0

b=5m, a=k, and c=9k

25m^2-4(k)(9k)=0

25m^2-36k^2=0

25m^2=36k^2

25/36=k^2/m^2

5/6=k/m

k=5 and m=6

5x^2+30x+45=0

x^2+6x+9=0

(x+3)^2=0

(x+3)(x+3)=0

x+3=0

x=-3