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JEE Main 2014 · 12 Apr · Shift 1, Mathematics question 63

The sum of the roots of the equation, x2+∣2x−3∣−4=0x^2+|2x-3|-4=0, is :

Choose one option
Answer and worked solution

Official answer: C

  • x≥32x\ge\frac32: x2+2x−7=0x^2+2x-7=0 gives x=−1+22≈1.83x=-1+2\sqrt2\approx1.83 (valid).
  • x<32x<\frac32: x2−2x−1=0x^2-2x-1=0 gives x=1−2x=1-\sqrt2 (valid; 1+21+\sqrt2 is rejected).

Sum: −1+22+1−2=2-1+2\sqrt2+1-\sqrt2=\sqrt2.

Topics:Equations reducible to quadraticInequalities and modulus
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