A) \[{{(a+c)}^{2}}<{{b}^{2}}\]
B) \[(a+{{c}^{2}})={{b}^{2}}\]
C) \[{{(a+c)}^{2}}>{{b}^{2}}\]
D) \[({{a}^{2}}+c)={{b}^{2}}\]
Correct Answer: C
Solution :
\[\because \] The equation has no real roots. \[\therefore \] \[{{b}^{2}}-4ac<0\Rightarrow \,4ac>{{b}^{2}}\] ?(i) Also, \[{{(a-c)}^{2}}\ge 0\Rightarrow \,{{a}^{2}}+{{c}^{2}}\ge 2ac\] ?(ii) On adding these two inequalities, we get \[{{a}^{2}}+{{c}^{2}}+2ac>{{b}^{2}}\] \[\Rightarrow \,\,{{(a+c)}^{2}}>{{b}^{2}}\]You need to login to perform this action.
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