• # question_answer ) Which of the following equations has two distinct real roots? A)  $2{{x}^{2}}-3\sqrt{2}x+\frac{9}{4}=0$B)  ${{x}^{2}}+x-5=0$C)  ${{x}^{2}}+3x+2\sqrt{2}=0$D) $5{{x}^{2}}-3x+1=0$

(A) $2{{x}^{2}}-3\sqrt{2}x+\frac{9}{4}=0$ $D={{b}^{2}}-4ac=18-4(2)\left( \frac{2}{9} \right)=18-18=0$ $\therefore$   Given have equal roots. (B)   ${{x}^{2}}+x-5=0~$ $D=1-4(1)(-5)=1+20=21>0$ $\therefore$ Given equation has real and distinct roots.      (C) ${{x}^{2}}+3x+2\sqrt{2}=0$             $D={{(3)}^{2}}-4(1)(2\sqrt{2})=9-8\sqrt{2}<0$ $\therefore$ Given equation does not have real roots. (D)   $5{{x}^{2}}-3x+1=0$           $D={{(-3)}^{2}}-4(5)(1)=9-20=-11<0$ $\therefore$ Given equation does not have real roots.