A) \[\pm \,1\]
B) \[\pm \,2\]
C) \[\pm \,3\]
D) \[\pm \,4\]
Correct Answer: D
Solution :
Let the common root be \[\alpha ,\] then \[{{\alpha }^{2}}-k\alpha -21=0\] ?(i) and \[{{\alpha }^{2}}-3k\alpha +35=0\] ?(ii) On solving by the rules of cross multiplication \[\frac{\alpha }{-35-63k}=\frac{\alpha }{-21-35}=\frac{1}{-3k+k}\] \[\therefore \] \[\alpha =\frac{-98k}{-56}=\frac{7k}{4}\] and \[\frac{7k}{4}=\frac{28}{k}\] \[\Rightarrow \] \[7{{k}^{2}}=28\times 4\] \[\therefore \] \[k=\pm 4\]
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