Question

求下列函數(shù)的零點：
(1)y=x³-7x+6;(2)y=x+-3.

Answer 1

（1）函數(shù)y=x³-7x+6的零點為-3,1,2（2）函數(shù)y=x+-3的零點為1，2

（1）∵x³-7x+6=(x³-x)-(6x-6)
=x(x²-1)-6(x-1)=x(x+1)(x-1)-6(x-1)
=(x-1)(x²+x-6)=(x-1)(x-2)(x+3)
解x³-7x+6=0,即(x-1)(x-2)(x+3)=0
可得x₁=-3,x₂=1,x₃=2.
∴函數(shù)y=x³-7x+6的零點為-3,1,2.
(2)∵x+
解x+即=0,可得x=1或x=2.
∴函數(shù)y=x+-3的零點為1，2.