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对于一元二次方程,除了讨论根的性质符号外,往往还要求讨论它的根的分布范围。要求出一元二次方程的根落在某区间的内或外的充要条件,通常要借助于二次函数的图象.本文将对零值定理在二次函数中的应用作一些探讨. 零值定理:设f(x)是闭区间[a,b]上的连续函数,且f(a)f(b)<0,则必存在c∈(a,b),使得f(c)=0. 众所周知,一元二次函数f(x)=ax~2+bx+c(不妨设a>0)是实数集上的连续函数,因此,我们可用零值定理研究它的性质.
For the quadratic equation of one yuan, in addition to discussing the nature of the root symbol, it is often required to discuss the distribution range of its root. The necessary and sufficient condition for the root of a quadratic equation to fall within or outside of a certain interval is usually the image of a quadratic function. This paper will discuss some applications of the zero-value theorem in the quadratic function. Value Theorem: Let f(x) be a continuous function on the closed interval [a,b], and if f(a)f(b)<0, then there must exist c∈(a,b) so that f(c)= 0. It is well known that the unary quadratic function f(x)=ax~2+bx+c (may be set a>0) is a continuous function on a real number set. Therefore, we can study its properties using the zero-value theorem.