No AI is used
  1. 홈
  2. 계산기
  3. 계산기: 대수학 I
  4. 대수 계산기

데카르트의 부호법칙 계산기

데카르트의 부호법칙을 단계별로 적용하기

이 계산기는 데카르트의 부호법칙을 사용하여 주어진 다항식의 양의 및 음의 실근의 최대 개수를 단계별로 구해 보여 줍니다.

Enter a polynomial:

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

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.