SOLUTION: for what value(s) of k does kt^2 - 6t + k = 0 have imaginary roots?
Algebra.Com
Question 239516: for what value(s) of k does kt^2 - 6t + k = 0 have imaginary roots?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Strictly speaking, from the way you worded your question, there are no real values of 
for which 
has purely imaginary roots. That is because the coefficient on the 1st degree term is non-zero and rational, hence any roots of the given equation must have a rational (and therefore real) component. There is a range of values for for which will have a pair of complex roots of the form 
where 
and 
.
Remember the discriminant: 
If 
then the roots are a conjugate pair of complex numbers of the form . Only in the case where 
is the real part of the complex number equal to zero and the complex number purely imaginary.
So:
^2\ -\ 4(k)(k))
And for , 
, hence 
or 
.
Actually it is possible to have purely imaginary roots if you allow 
, but somehow I don't think that is what you were talking about when you asked the question.
John
RELATED QUESTIONS
for what value of k does the equation kt^2 + 5t +2 = 0, have exactly one real solution... (answered by stanbon)
What value of K will the roots of the equation 2x^2-3x+K=0 be imaginary? (answered by Theo)
For what values of k does the equation 3x^2-2x+k=0 have imaginary roots?
1. k is less... (answered by ptaylor)
For what value(s) of K will the equation 3xsquared=k-2x have real... (answered by stanbon)
Find all real values of K for which 3t^2-4t+k=0 has imaginary... (answered by solver91311)
For what value of k does x^2 + kx + 1 = 0 have two different real roots?
This is what (answered by Boreal)
For what values of k does x^2+kx+7=0 have no real... (answered by Alan3354)
For what value of k are the roots of 2x^2-8x+k=0... (answered by robertb)
What should be the range of the value of k so that the equation 2x2+3kx-9=0 will have... (answered by KMST)