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

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(c) Given eqn ${x^3} + 3Hx + G = 0$ and $G$ and $H$ are real and ${G^2} + 4{H^3} > 0$.

Let $\alpha ,\beta $ be the roots of given cubic equation

Vedclass · Accepted Answer

One real and two imaginary

Vedclass · Answer

(c) Given eqn ${x^3} + 3Hx + G = 0$ and $G$ and $H$ are real and ${G^2} + 4{H^3} > 0$.

Let $\alpha ,\beta $ be the roots of given cubic equation.

We know that $\alpha = {\left( {\frac{{ - G + \sqrt {{G^2} + 4{H^3}} }}{2}} \right)^{1/3}}$ and $\beta = {\left( {\frac{{ - G - \sqrt {{G^2} + 4{H^3}} }}{2}} \right)^{1/3}}$, since ${G^2} + 4{H^3}> 0,$

therefore the cubic equation has got one real and two imaginary roots.

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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