Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation
If three quadratic equations x^2+( A B+A C ) x+ B C 4 =0, x^2+( B C+A B ) x+ A C 4 =0 and x^2+( A C+B C ) x+ A B 4 =0 are given, where A , B , C are three points in a plane then -
Options
- Aif A , B , C are making a triangle then all equations have real & distinct roots.
- Bif A , B , C are collinear, then all equations have real & equal roots.
- Cif A, B, C are collinear, then two equations have real & distinct, one equation has real & equal roots.
- Dfor every position of A , B , C all six roots are negative.
Correct answer
D. for every position of A , B , C all six roots are negative.
Step-by-step solution
aligned & D₁=(A B+A C)-B C ; D₃=(A C+B C)-A B & D₂=(B C+A B)-A C ; for all are + ve ( Distinct & & real ) aligned If collinear then let AB + BC = AC D₃=0 & all others will be +ve . array l + =- ve =+ ve array in each case both roots are negative