The sum of the squares of all the roots of the equation \(x^{2}+|x+4|+|x-4|-35=0\) is
Question and options
The sum of the squares of all the roots of the equation is
- 74
- 175
- 50
- 148
Answer and explanation
Correct answer: C - 50
For |x|>=4, |x+4|+|x-4|=2|x|: x^2+2|x|-35=0 gives |x|=5 (valid), roots +-5. For |x|<4 the sum is 8: x^2=27, |x|=5.2 not <4, rejected. Sum of squares = 25+25 = 50.
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IPMAT Indore
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