A) \[\frac{q+\beta }{a+p}\]
B) \[\frac{q-\beta }{a+p}\]
C) \[\frac{q-\beta }{a-p}\]
D) none of these
Correct Answer: C
Solution :
Let \[\alpha \]be the common root of the equations \[{{x}^{2}}+ax+\beta =0\]and \[{{x}^{2}}+px+q=0\] \[\Rightarrow \]\[{{\alpha }^{2}}+a\alpha +\beta =0\]and \[{{\alpha }^{2}}+p\alpha +q=0\] \[\therefore \] Both equations represents a same line \[\Rightarrow \] \[\frac{{{\alpha }^{2}}}{aq-p\beta }=\frac{-\alpha }{q-\beta }=\frac{1}{p-a}\] \[\Rightarrow \] \[\alpha =\frac{q-\beta }{a-p}\]
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