Find all real values of the parameter a for which the equation
(a-1)z^{4}-4z^{2} +a+2=0
has only pure imaginary roots.
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7 Answers
62Hint: this is same as having 2 -ve roots to the equation
(a-1)t2-4t+a+2=0
1i tried to do it that way
but ans is not correct
t<0
:. frac{(4+2(6-a^{2}-a)^{0.5})}{2(a-1)} is <0
also a<1
so it comes smthing else than
[-3,-2]
1i got
a<1
and a< -2
but i'm nt getting a>-3
using c/a>0 and -b/a <0
wt was wrong with the prev method???
62frac{(4+2(6-a^{2}-a)^{0.5})}{2(a-1)} is <0
I did not understand why you reached this conclusion!
Am i missnig something..
What you should do is divide the whole thing by (a-1)
Then you will want sum of roots to be -ve,
Product to be +ve
And you will also want real roots... (D>0)
Am I missing something?
62is it avinav..
Then what does the first step mean? I think i am sleeping :D
1thanks
ya i missed D>0
by the way
that fract......was
i jst took the roots of the quadratic equation to be negative and wrote
(-B (+-)\sqrt{B^{2}-4AC})/2*A <0
THANKS