笛卡兒變號法則計算器
逐步應用笛卡兒符號法則
此計算器將根據笛卡兒變號法則，找出給定多項式的正、負實根的最大個數，並顯示步驟。
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.