A) \[{{p}^{2}}-{{q}^{2}}=0\]
B) \[{{p}^{2}}+{{q}^{2}}=2q\]
C) \[{{p}^{2}}+p=2q\]
D) None of these
Correct Answer: C
Solution :
Let the roots be a and b Þ \[\alpha +\beta =-p\], \[\alpha \beta =q\] Given, \[\alpha +\beta ={{\alpha }^{2}}+{{\beta }^{2}}\] But \[\alpha +\beta ={{(\alpha +\beta )}^{2}}-2\alpha \beta \] \[\Rightarrow -p={{(-p)}^{2}}-2q\] \[\Rightarrow {{p}^{2}}-2q=-p\] \[\Rightarrow {{p}^{2}}+p=2q\].
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