Complex Numbers And Quadratic Equations question 678
Question: The real roots of the equation $ x^{2}+5|x|+4=0 $ are
Options:
A) $ {-1,-4} $
B) $ {1,4} $
C) $ {-4,4} $
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
Case 1: $ x \ge 0 $
$ \therefore the equation becomes x^{2}+5x+4=0 $ or $ x=-1,-4but x\ge 0 $
$ \therefore $ both values, non-admissible: Case 2: $ x \le 0 $ The eqn becomes $ {x^{2}}- 5x + 4 = 0 or x = 1,4 $ both values are non-admissible,
$ \therefore $ No real roots. Alternatively, since $ {x^{2}} \ge 0; | x | \ge 0 $
$ \therefore x^{2} + | x | + 4 > 0 for all x \in R $
$ \therefore x^{2} + | x | + 4 \ne 0 for all x \in R $
BETA
