) cho đa thức f(x) =ax2 +bx +c. Biết f(0)= 2017; f(1) =2018; f(-1)= 2019. Tính f(2) 11/10/2021 Bởi Camila ) cho đa thức f(x) =ax2 +bx +c. Biết f(0)= 2017; f(1) =2018; f(-1)= 2019. Tính f(2)
f(0)= a0²+b0+c=2017 ⇒c=2017 f(1) =a1²+b1+c=2018 ⇒a+b=2018-c=2018-2017=1 f(-1)=a(-1)²+b(-1)+c= 2019 ⇒a-b=2019-c=2019-2017=2 ⇒a=(1+2) :2=1,5 ⇒b=(1-2) :2=-0,5 vậy f(2)=1,5.2²-0,5.2+2017 =6-1+2017 =2022 vậy f(2)=2022 Bình luận
`f(0)=a.0+b.0+c=c=2017` `f(1)=a.1+b.1+c=a+b+c=2018` `⇒f(1)-f(0)=a+b+c-c=a+b=2018-2017=1` `⇒a=1-b` `f(-1)=a.(-1)^2+b.(-1)+c=a-b+c=2019` `⇒f(-1)-f(0)=a-b+c-c=a-b=1-b-b=1-2b=2019-2017=2` `⇔2b=-1` `⇔b=-0,5` mà `a=1-b` `⇒a=1-(-0,5)=1,5` `⇒f(2)=1,5.2^2-0,5.2+2017=2012` Bình luận
f(0)= a0²+b0+c=2017
⇒c=2017
f(1) =a1²+b1+c=2018
⇒a+b=2018-c=2018-2017=1
f(-1)=a(-1)²+b(-1)+c= 2019
⇒a-b=2019-c=2019-2017=2
⇒a=(1+2) :2=1,5
⇒b=(1-2) :2=-0,5
vậy f(2)=1,5.2²-0,5.2+2017
=6-1+2017
=2022
vậy f(2)=2022
`f(0)=a.0+b.0+c=c=2017`
`f(1)=a.1+b.1+c=a+b+c=2018`
`⇒f(1)-f(0)=a+b+c-c=a+b=2018-2017=1`
`⇒a=1-b`
`f(-1)=a.(-1)^2+b.(-1)+c=a-b+c=2019`
`⇒f(-1)-f(0)=a-b+c-c=a-b=1-b-b=1-2b=2019-2017=2`
`⇔2b=-1`
`⇔b=-0,5`
mà `a=1-b`
`⇒a=1-(-0,5)=1,5`
`⇒f(2)=1,5.2^2-0,5.2+2017=2012`