A) \[\frac{q-\beta }{\alpha -p}\]
B) \[\frac{p\beta -\alpha q}{q-\beta }\]
C) \[\frac{q-\beta }{\alpha -p}\]or \[\frac{p\beta -\alpha q}{q-\beta }\]
D) None of these
Correct Answer: C
Solution :
Let the common root be y. Then \[{{y}^{2}}+py+q=0\] and \[{{y}^{2}}+\alpha \text{ }y+\beta =0\] On solving by cross multiplication, we have \[\frac{{{y}^{2}}}{p\beta -q\alpha }=\frac{y}{q-\beta }=\frac{1}{\alpha -p}\] \ \[y=\frac{q-\beta }{\alpha -p}\]and \[\frac{{{y}^{2}}}{y}=y=\frac{p\beta -q\alpha }{q-\beta }\]
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