Solve the following quadratic equation: x^2-(2 b-1) x+ (b^2-b-20 … - Vidyadip

Question

Solve the following quadratic equation:
$ x^2-(2 b-1) x+\left(b^2-b-20\right)=0 $

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Answer

$ x^2-(2 b-1) x+\left(b^2-b-20\right)=0 $
$ \Rightarrow x^2-(2 b-1) x+\left(b^2-5 b+4 b-20\right)=0 $
$ \Rightarrow x^2-(2 b-1) x+[b(b-5)+4(b-5)]=0 $
$ \Rightarrow x^2-(2 b-1) x+(b-5)(b+4)=0 $
$ \Rightarrow x^2-(2 b-1) x-(b+4) x+(b-5)(b+4)=0 $
$ \Rightarrow x[x-(b-5)]-(b+4)[x-(b-5)]=0 $
$ \Rightarrow[x-(b-5)][x-(b+4)]=0 $
$ \Rightarrow x-(b-5)=0 \text { or } x-(b+4)=0 $
$ \Rightarrow x=b-5 \text { or } x=b+4$

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