1.
α+β=-p-----⑴
α*β=q------⑵
⑴⑵得
则有p^2=2q+1
2.让α=sina,β=cosa(a∈[0,2π])
f(p)=(p^2-1)/2=q
可化成sina*cosa=(2sin(a+π/4)^2-1)/2=q
a+π/4∈[π/4,9π/4 ]
则sin(a+π/4)^2最大值为1,最小值为0
所以q最大值为1/2,最小值为-1/2
已知方程x^2+px+q=0两实数根分别为α,β且满足α^2+β^2=1
已知方程x^2+px+q=0两实数根分别为α,β且满足α^2+β^2=1
1.求p与q满足的关系式
2.求函数q=f(p)的最大和最小值
1.求p与q满足的关系式
2.求函数q=f(p)的最大和最小值
数学人气:211 ℃时间:2020-03-28 13:17:57
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