10th Class Mathematics Quadratic Equations Question Bank Quadratic Equations

  • 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) \[5{{x}^{2}}-3x+1=0\]               

    Correct Answer: B

    Solution :

    (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.

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