二次函数f(x)=px^2+qx+r中实数p、q、r满足p/(m+2)+q/(m+1)+r/m=0,其中m>0.求证:(1)pf(m/(m+1))<0
人气:205 ℃ 时间:2019-09-22 07:16:17
解答
∵p/(m+2)+q/(m+1)+r/m=0
∴(p^2)m/(m+2)+pqm/(m+1)+pr=0
∴pqm/(m+1)+pr=-(p^2)m/(m+2)
pf(m/(m+1))
=p[p[m/(m+1)]^2+q[m/(m+1)]+r]
=[pm/(m+1)]^2+pqm/(m+1)+pr
=[pm/(m+1)]^2-(p^2)m/(m+2) {代入上式结论}
=(p^2)m[m/(m+1)^2-1/(m+2)]
=(p^2)m{[m(m+2)-(m+1)^2]/(m+2)(m+1)^2}
=(p^2)m[(-1)/(m+2)(m+1)^2]
=-(p^2)m[1/(m+2)(m+1)^2]<0
推荐
- 二次函数f(x)=px^2+qx+r中实数p、q、r、满足
- 已知p,q是非零实数,集合A={x|x^2+px+q=0},B={x|qx^2+px+1=0}同时满足
- 已知二次函数f(X)=X^2+px+q当f(x)
- m,n,p,q都是实数,而且p×q=2(m+n).求证:x²+px+m=0,x²+qx+n=0.求证这两个方程中至少有一个方程有实数根(请写出过程)
- 设二次函数f(x)=x2+px+q,集合A={x| f(x)=x,x∈R},集合B={x| f(x-1)=x+1,x∈R},当A={2}时,求集合B.
- 如图,圆O的直径AB长为6,弦AC长为2,∠BAC的平分线交圆O于点D,求四边形ADBC的面积
- 含消化酶种类最多的消化液是一圈分泌的___和___分泌的___,而不含消化酶的消化液是___分泌的____.
- so seriously --------------in the train accident that he has lost his memory of anything
猜你喜欢