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  • Which of the following is not a quadratic equation? (A)2(x-1)^{2}=4x^{2}-2x+1(B)2x-x^{2}=x^{2}+5 (D)(x^{2}+2x)^{2}=x^{4}+3+4x^{3}

Which of the following is not a quadratic equation?

\\(A)2(x-1)^{2}=4x^{2}-2x+1\\ (B)2x-x^{2}=x^{2}+5\\ (C)(\sqrt{2}x+\sqrt{3})^{2}+x^{2}=3x^{2}-5x\\ (D)(x^{2}+2x)^{2}=x^{4}+3+4x^{3}

Answers (1)

 (C)(\sqrt{2}x+\sqrt{3})^{2}+x^{2}=3x^{2}-5x

Quadratic equation: A quadratic equation in x is an equation that can be written in the standard form ax^{2} + bx + c = 0, a \neq 0

 Where a, b and c are real numbers

  2(x-1)^{2}=4x^{2}-2x+1

  2(x^{2}+1-2x)=4x^{2}-2x+1              

[using (a – b)2 = a2 + b2 – 2ab]
  \\2x^{2}+2-4x-4x^{2}+2x-1=0\\ -2x^{2}-2x+1=0

It is a quadratic equation because it is in the form

ax^{2} + bx + c = 0

(B)       

        \\2x-x^{2}=x^{2}+5\\ 2x-x^{2}-x^{2}-5=0\\ -2x^{2}+2x-5=0\\ -2x^{2}+2x-5=0      

      It is a quadratic equation because it is in the form ax^{2} + bx + c = 0

(C)     
(\sqrt{2}x+\sqrt{3})^{3}+x^{2}=3x^{2}-5x\\ (\sqrt{2}x)^{2}+(\sqrt{3})^{2}+2(\sqrt{2}x)(\sqrt{3})+x^{2}=x^{2}-5x      \left [using \;(a+b)^{2}=a^{2}+b^{2}+2ab \right ]

2x^{2}+3+2\sqrt{6}x+x^{2}-3x^{2}+5x=0\\ (2\sqrt{6}+5)x+3=0

        It is not in the form of ax^{2} + bx + c = 0

            Hence it is not a quadratic equation.

(D)     
            (x^{2} + 2x)^{2} = x^{4} + 3 + 4x^{3}\\ (x^{2})^{2} + (2x)^{2} + 2(x^{2})(2x) = x^{4} + 3 + 4x^{3}     \left [using \;(a+b)^{2}=a^{2}+b^{2}+2ab \right ]
            x^{4} + 4x^{2} + 4x^{3} - x^{4} - 3 - 4x^{3} = 0\\ 4x^{2}-3=0

            It is in the form of ax^{2} + bx + c = 0

            Hence it is a quadratic equation

            Only option (C) is not in the form of ax^{2} + bx + c = 0

            Hence (C) is not a quadratic equation.

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