If two equations a_ 1 x^ 2 +b_ 1 x+c_ 1 =0 and a_ 2 x^ 2 +b_ 2 x+c_ 2 =0 have a common…

Mathematics · JEE Main · NTA ExamsComplex Numbers and Quadratic Equations

If two equations \(a_{1} x^{2}+b_{1} x+c_{1}=0\) and \(a_{2} x^{2}+b_{2} x+c_{2}=0\) have a common root, then the value of \(\left(a_{1} b_{2}-a_{2} b_{1}\right] \cdot\left[b_{1} c_{2}-b_{2} c_{1}\right]\) is

 

  1. \(-\left[a_{1} c_{2}-a_{2} c_{1}\right]^{2}\)
  2. \(\left(a_{1} a_{2}-c_{1} c_{2}\right)^{2}\)
  3. \(\left(a_{1} c_{1}-a_{2} c_{2}\right)^{2}\)
  4. \(\left(a_{1} c_{2}-c_{1} a_{2}\right)^{2}\)

Answer

(D) (a_ 1 c_ 2 -c_ 1 a_ 2 )^ 2

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