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

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(C) For a cubic equation of the form ${x^3} + px + q = 0$,the discriminant is given by $\Delta = - (4p^3 + 27q^2)$.Comparing ${x^3} + 3Hx + G = 0$ wit

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One real and two imaginary

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(C) For a cubic equation of the form ${x^3} + px + q = 0$,the discriminant is given by $\Delta = - (4p^3 + 27q^2)$.Comparing ${x^3} + 3Hx + G = 0$ with the standard form,we have $p = 3H$ and $q = G$.The discriminant is $\Delta = - (4(3H)^3 + 27G^2) = - (108H^3 + 27G^2) = - 27(4H^3 + G^2)$.Given that ${G^2} + 4{H^3} > 0$,it follows that $\Delta = - 27(G^2 + 4H^3) For a cubic equation with real coefficients,if the discriminant $\Delta Therefore,the correct option is $(c)$.

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

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