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What is the sum of roots of equation x^2 + |2x-3| - 4 = 0

What is the sum of roots of equation x^2 + |2x-3| - 4 = 0

Grade:12

1 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
8 years ago
First case x>=3/2

x^2 + 2x – 3 -4 =0
x^2 + 2x -7 =
x= (-2 ±\sqrt{32})/2 = -1 ± 2\sqrt{2} only -1 + 2\sqrt{2}>3/2

Second case x<3/2
x^2 + 3-2x -4=0
x^2 -2x -1 =0
x= (2 ± 2\sqrt{2})/2 = 1 ±\sqrt{2}
Only 1-\sqrt{2}is less than 3/2
So sum of roots is -1 +2\sqrt{2}+ 1 –\sqrt{2}=\sqrt{2}

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