Complex Numbers And Quadratic Equations question 166
Question: For the equation $ |x^{2}|+|x|-6=0 $ , the roots are [EAMCET 1988, 93]
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 $ \ 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 $ , \ $ x=2 $ is the solution. Hence $ x=2 $ , $ -2 $ are the solutions and their sum is zero. Aliter: $ |x^{2}|+|x|-6=0 $
Þ $ (|x|+3)(|x|-2)=0 $
Þ $ |x|=-3 $ , which is not possible and $ |x|=2 $
Þ $ x=\pm 2 $ .
BETA
