同理, q 是4 的约数。 考虑到 p,q 互质, q=\pm1 分别代入即可, q=1 时, a^2+4b^2+5=0 ,矛盾。 q=-1 ,也就是 a^2-4b^2+3=0 (2b+a)(2b-a)=3 (a,b)=(1,1),(-1,1),(-1,-1),(1,-1) 其实就是有理根定理了……详细请点进: 不用卡丹公式,一元三次方程如何巧解...
Discover what the rational root theorem is and what rational roots are. Using examples, understand how the rational root theorem is helpful in...
Also, we will solve some problems using the same.What is the Rational Root Theorem?The rational root theorem is also known as the rational zero theorem (or) the rational zero test (or) rational test theorem and is used to determine the rational roots of a polynomial function. The general ...
(x)=0. The Rational Root Theorem ~ states that If P(x) is a polynomial with integer coefficients and if is a zero of P(x) then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x). Using this theorem we can find all the ...
The theorem that, if a rational number p / q, where p and q have no common factors, is a root of a polynomial equation with integral coefficients, then the coefficient of the term of highest order is divisible by q and the coefficient of the term of lowest order is divisible by p.Mc...
Rational root theorem Let anxn + an-1xn-1 + ... + a1x + a0 = 0 be a polynomial equation with integer coefficients. If p/q is in simplest form and is a rational root of the polynomial equation, then p must be a factor of a0 and q must be a factor of an...
rootRoot 系统标签: rationaltheoremrootpolynomialzerosequation RationalRootTheoremRecap:Whatweknow•#ofchangesindirectionforapolynomialfunction:•MaximumnumberofZeros:•EndBehaviorofaPolynomialGraphEndBehavior•Positivecoefficient,EvenDegree•NegativecoefficientEvenDegree•PositivecoefficientOddDegree•Negativecoeffi...
According to the rational root theorem, how many possible rational roots are there to 2 x^4 + 14 x^3 - 6 x + 7 = 0? How many possible rational roots are there for 2x^4 + 4x^3 - 6x^2 + 15x - 12 = 0? Use the rational roots theorem to factor de...
有理根定理(Rational Root Theorem) 是试根法的一部分,用于简化试根法,帮助我们排除大部分不可能的值,减少计算量。因为是基础知识点,这里直接就给定义了: Letf(x)be the polynomialf(x)=anxn+an−1xn−1+an−2xn−2+...+a1x+a0, where all theaiare integers and bothananda0are nonzero. If...
有理根定理，这个概念在九州大学2018年高考理科第四题中有所体现。该题考察的是整数与特定公式的关系，要求我们利用这个定理来分析一个函数。该定理指出，如果一个多项式的有理根可以表示为分数形式，其分母只能是原多项式系数的公约数，而分子则为一个整数。题目中，首先通过观察[公式]和[公式]的关系，...