A) \[9{{p}^{2}}=2q\]
B) \[2{{q}^{2}}=9p\]
C) \[2{{p}^{2}}=9q\]
D) \[9{{q}^{2}}=2p\]
Correct Answer: C
Solution :
Let \[\alpha ,\beta \] are roots of \[{{x}^{2}}+px+q=0\] So \[\alpha +\beta =-p\]and \[\alpha \beta =q\] Given that \[(\alpha +\beta )=3(\alpha -\beta )=-p\]Þ\[\alpha -\beta =\frac{-p}{3}\] Now \[{{(\alpha -\beta )}^{2}}={{(\alpha +\beta )}^{2}}-4\alpha \beta \] Þ \[\frac{{{p}^{2}}}{9}={{p}^{2}}-4q\]or \[2{{p}^{2}}=9q\].
You need to login to perform this action.
You will be redirected in
3 sec
