In the equation x^3 + 3Hx + G = 0,if G and H | vedclass

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(C) The given cubic equation is $x^3 + 3Hx + G = 0$,where $G$ and $H$ are real constants.For a cubic equation of the form $x^3 + px + q = 0$,the discr

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One real and two imaginary

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(C) The given cubic equation is $x^3 + 3Hx + G = 0$,where $G$ and $H$ are real constants.For a cubic equation of the form $x^3 + px + q = 0$,the discriminant is given by $\Delta = - (4p^3 + 27q^2)$.In our case,$p = 3H$ and $q = G$.Substituting these,we get $\Delta = - (4(3H)^3 + 27G^2) = - (108H^3 + 27G^2) = -27(4H^3 + G^2)$.Given that $G^2 + 4H^3 > 0$,it follows that $\Delta = -27(G^2 + 4H^3) For a cubic equation with real coefficients,if the discriminant $\Delta < 0$,the equation has one real root and two complex conjugate (imaginary) roots.

In the equation $x^3 + 3Hx + G = 0$,if $G$ and $H$ are real and $G^2 + 4H^3 > 0$,then the roots are

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