come in若a
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comein若acomein若acomein若a此处是否是“t不等于-1”?若是如此,则关于x的方程(x-a)(x-c)+t(x-b)(x-d)=0为一个一元二次方程.令f(x)=(x-a)(x-c)
come in若a
come in
若a
come in若a
此处是否是“t不等于-1”?若是如此,则关于x的方程(x-a)(x-c)+t(x-b)(x-d)=0为一个一元二次方程.令f(x)=(x-a)(x-c)+t(x-b)(x-d)(x是实数)得到一个二次函数.当t为正数时,有f(a)=t(a-b)(a-d)仍为正数,f(c)=t(c-b)(c-d)为负数,函数图象与x轴有两个交点,故方程(x-a)(x-c)+t(x-b)(x-d)=0有两个不相等的实根;当t为负数时,同理可得,方程(x-a)(x-c)+t(x-b)(x-d)=0有两个不相等的实根.综合可知,对于任意实数t(t不等于-1),关于x的方程(x-a)(x-c)+t(x-b)(x-d)=0都有两个不相等的实数根.(当t等于-1时,方程只有一个实根)
come in若a
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