if one root of the equation 2x^2-kx+k =0 be twice the other, find the value of k.
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comparing with ax^2+bx+ c=0
a=2,b=-k,c=k
let the roots be x&y respectively.
x=2y.........................(given)
x+y=-b/a
put x=2y
2y+y=-(-k)/2
3y=k/2
k= 6y....................(multiplying by 2 to both sides)y=6/k......,,(1)
now,
x*y=c/a
2y*y=k/2
2y^2=k/2
4y^2=k
4(6/k)^2=k
4(36/k^2)=k
144/k=0
k=144
a=2,b=-k,c=k
let the roots be x&y respectively.
x=2y.........................(given)
x+y=-b/a
put x=2y
2y+y=-(-k)/2
3y=k/2
k= 6y....................(multiplying by 2 to both sides)y=6/k......,,(1)
now,
x*y=c/a
2y*y=k/2
2y^2=k/2
4y^2=k
4(6/k)^2=k
4(36/k^2)=k
144/k=0
k=144
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