Which of the following equations has no real | vedclass

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(D) To determine if a quadratic equation $ax^2 + bx + c = 0$ has real roots,we calculate the discriminant $D = b^2 - 4ac$. If $D < 0$,the equation has

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$x^2 - 4x + 3\sqrt{2} = 0$

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(D) To determine if a quadratic equation $ax^2 + bx + c = 0$ has real roots,we calculate the discriminant $D = b^2 - 4ac$. If $D $A)$ For $3x^2 + 4\sqrt{3}x + 4 = 0$,$D = (4\sqrt{3})^2 - 4(3)(4) = 48 - 48 = 0$. Since $D = 0$,it has real and equal roots.$B)$ For $x^2 - 4x - 3\sqrt{2} = 0$,$D = (-4)^2 - 4(1)(-3\sqrt{2}) = 16 + 12\sqrt{2} > 0$. It has real and distinct roots.$C)$ For $x^2 + 4x - 3\sqrt{2} = 0$,$D = (4)^2 - 4(1)(-3\sqrt{2}) = 16 + 12\sqrt{2} > 0$. It has real and distinct roots.$D)$ For $x^2 - 4x + 3\sqrt{2} = 0$,$D = (-4)^2 - 4(1)(3\sqrt{2}) = 16 - 12\sqrt{2}$. Since $\sqrt{2} \approx 1.414$,$12\sqrt{2} \approx 16.968$. Thus,$D = 16 - 16.968 = -0.968 < 0$. Therefore,this equation has no real roots.

Which of the following equations has no real roots?

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