A) \[\sqrt{\frac{bc}{a}}\]
B) \[a{{c}^{2}}\]
C) \[\frac{b}{a}\]
D) \[\sqrt{\frac{c}{a}}\]
Correct Answer: D
Solution :
\[\alpha ,\beta \] are the roots of \[a{{x}^{2}}+bx+c=0\] |
\[\therefore \,\,\,\,\alpha +\beta =-b/a\] and \[\alpha \beta =c/a\] |
Circle passes through \[\left( \alpha ,0 \right)\] and \[\left( \beta ,0 \right)\], \[OA=\alpha ,OB=\beta \] |
\[\because \] OT is tangent of circle |
\[\therefore \,\,O{{T}^{2}}=OA.OB\] \[\Rightarrow \,\,O{{T}^{2}}=\alpha \beta \] \[\Rightarrow \,\,OT=\sqrt{\alpha \beta }\] \[\Rightarrow \,\,OT=\sqrt{c/a}\] |
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