Complex Numbers And Quadratic Equations question 710
Question: For the equation $ | x^{2} |+| x |-6=0, $ the roots are
Options:
A) One and only one real number
B) Real with sum one
C) Real with sum zero
D) Real with product zero
Show Answer
Answer:
Correct Answer: C
Solution:
When $ x<0,| x |=-x $
$ \therefore $ Equation is $ {x^{2}}-x-6=0 \Rightarrow x = -2,3 $ $ \because x < 0, \therefore x = -2 $ is the solution. When $ x\ge 0,| x |=x $
$ \therefore Equation is x^{2} + x- 6 = 0 \Rightarrow x = 2, -3 $ $ \because x \ge 0, \therefore x= 2 $ is the solution, Hence $ x = 2, -2 $ are the solutions and their sum is zero.
BETA
