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find the condition on \lambda such that this eqn has real roots
f(x) = \sqrt{3}\lambda x^4 - x^3 + 3\sqrt{3}\lambda
According to the descartes rule,this eqn has either 2 or 0 roots,but i'm not getting any further frm here
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12 Answers
21vivek, do u hav the answer???
if yes , pl. hide n post it........
11Simpler method
Let a2 = x4
therefore the equation becomes
a2λ√3 - a +λ3√3
a = 1 ± √(1 -4*λ2*3*3)/2λ√3
Since we want real roots
a = x2
Therefore
1 -4*λ2*3*3>0
1> 4λ2*9
λ<±1/6
But we have to only consider positive part of this since There is λ in the demoninator
Now for - part
√1 -4*λ2*3*3>1
Therefore λ cannot take negative values
Possible values of λ range from (0,1/6)
1@virang, u said::::::
Let a2 = x4
therefore the equation becomes
a2λ√3 - a +λ3√3
the equation given is λ√3x4 - x3 +λ3√3
it is x3 not x2.
1y1=4√3λx3-3x2
if y1=0 then x=0 or x=√3/4λ
y2=12√3λx2-3
y2(0)<0
so, y2(√3/4λ) > 0 for max.. and min. both to exist....from here find the value of λ
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what I mean is that for y to have real; roots the graph shud look like this
