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Calculatrice de la règle des signes de Descartes

Appliquer la règle des signes de Descartes étape par étape

La calculatrice trouvera le nombre maximal de racines réelles positives et négatives du polynôme donné à l'aide de la règle des signes de Descartes, avec les étapes présentées.

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Solution

Your input: find the number of real roots of $$$x^{3} + 7 x^{2} + 4$$$ using the Descartes' Rule of Signs.

The rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or is less than it by an even number.

So, the coefficients are $$$1, 7, 4$$$.

As can be seen, there are $$$0$$$ changes.

This means that there are $$$0$$$ positive real roots.

To find the number of negative real roots, substitute $$$x$$$ with $$$- x$$$ in the given polynomial: $$$x^{3} + 7 x^{2} + 4$$$ becomes $$$- x^{3} + 7 x^{2} + 4$$$.

The coefficients are $$$-1, 7, 4$$$.

As can be seen, there is $$$1$$$ change.

This means that there is $$$1$$$ negative real root.

Answer

$$$0$$$ positive real roots.

$$$1$$$ negative real root.