Complex Numbers And Quadratic Equations question 681
Question: If both the roots of the equation $ x^{2}-2kx+k^{2}-4=0 $ lie between $ -3 $ and 5, then which one of the following is correct?
Options:
A) $ -2<k<2 $
B) $ -5<k<3 $
C) $ -3<k<5 $
D) $ -1<k<3 $
Show Answer
Answer:
Correct Answer: D
Solution:
$ {x^{2}}-2kx+k^{2}-4=0 $
$ \Rightarrow {{(x-k)}^{2}}-2^{2}=0 $
$ \Rightarrow ( x-k-2 )( x-k+2 )=0 $
$ \Rightarrow x=k+2,k-2 $
$ \Rightarrow k+2<5\And k-2>-3 $
$ \Rightarrow k<3\And k>-1 $
$ \Rightarrow -1<k<3 $
BETA
