A) 10
B) 20
C) 30
D) 40
Correct Answer: D
Solution :
Let a be a common root, then \[{{\alpha }^{2}}+a\alpha +10=0\] ?..(i) and \[{{\alpha }^{2}}+b\alpha -10=0\] ?..(ii) form (i) - (ii), \[(a-b)\alpha +20=0\Rightarrow \alpha =-\frac{20}{a-b}\] Substituting the value of a in (i), we get \[{{\left( -\frac{20}{a-b} \right)}^{2}}+a\,\left( -\frac{20}{a-b} \right)+10=0\] \[\Rightarrow 400-20\,a(a-b)+10{{(a-b)}^{2}}=0\] \[\Rightarrow 40-2{{a}^{2}}+2ab+{{a}^{2}}+{{b}^{2}}-2ab=0\] \[\Rightarrow \,{{a}^{2}}-{{b}^{2}}=40\].You need to login to perform this action.
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