Let α and β be the roots of x23x+c=0, where c is a real number. If α is a root of x2+3xc=0, find the value of αβ.


Answer:

0

Step by Step Explanation:
  1. α & β are the roots of the equation, therefore,
    αβ=c1=c  .....(1)
  2. As α is the root of the equation x23x+c=0,
    α23α+c=0  .....(2)
    Also, α is the root of the equation x2+3xc=0,
    (α)2+3(α)c=0α23αc=0.....(3)
  3. On subtracting eq(2) by eq(3), we get,
    α23αc(α23α+c)=0α23αcα2+3αc=02c=0c=0
  4. By eq(1), we have,
    αβ=cαβ=0

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