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JEE Main 2017 · Mathematics · Quadratic Equations · hard

If the equations x^2+ax+12=0, x^2+bx+15=0 and x^2+(a+b)x+36=0 have a common root, then ab equals

Single correct option

If the equations x2+ax+12=0x^2+ax+12=0, x2+bx+15=0x^2+bx+15=0 and x2+(a+b)x+36=0x^2+(a+b)x+36=0 have a common root, then abab equals
  1. A. 4848
  2. B. 5656
  3. C. 7272
  4. D. 6060
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Answer: (B) 5656

Let α\alpha be the common root. Adding the first two equations gives 2α2+(a+b)α+27=02\alpha^2+(a+b)\alpha+27=0. Subtracting the third equation α2+(a+b)α+36=0\alpha^2+(a+b)\alpha+36=0 from this yields α2−9=0\alpha^2-9=0, so α=±3\alpha=\pm3. For α=3\alpha=3: 9+3a+12=09+3a+12=0 gives a=−7a=-7 and 9+3b+15=09+3b+15=0 gives b=−8b=-8. For α=−3\alpha=-3 we get a=7, b=8a=7,\ b=8. Both cases satisfy the third equation and give ab=56ab=56.
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