SOLUTION: 1(a): If k=(x-1)²/x²+4,where k is a real number, show clearly that (k-1)x²+2x+(4k-1)=0 1(b): Hence find the value of k given that the equation (k-1)x²+2x+(4k-1)=0 has equal roo

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Question 401138: 1(a): If k=(x-1)²/x²+4,where k is a real number, show clearly that (k-1)x²+2x+(4k-1)=0
1(b): Hence find the value of k given that the equation (k-1)x²+2x+(4k-1)=0
has equal roots and k>0
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


1(a):

Since



And



Verification of these two steps is left as an exercise for the student.

Substituting:



Distribute and apply the common denominator:



Collect like terms:



1(b):

If



has equal roots, then



therefore for your equation:







From which we get that or

But is constrained to , hence is the desired value.

Check: and







Therefore equal roots.

John

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