Question

用秦九韶算法求多項(xiàng)式(x)=1+x+0.5x²+0.166 67x³+0.041 66x⁴+0.008 33x⁵,當(dāng)x=-0.2時(shí)的值.

Answer 1

【探究】根據(jù)秦九韶算法,把多項(xiàng)式改寫成如下形式：

f(x)=((((0.008 33x+0.041 66)x+0.166 67)x+0.5)x+1)x+1.

按照從內(nèi)到外的順序依次計(jì)算一次多項(xiàng)式當(dāng)x=-0.2時(shí)的值；

v₀=0.008 33;

v₁=0.008 33×(-0.2)+0.041 66=0.04;

v₂=0.04×(-0.2)+0.166 67=0.158 67;

v₃=0.158 67×(-0.2)+0.5=0.468 27;

v₄=0.468 27×(-0.2)+1=0.906 35;

v₅=0.906 35×(-0.2)+1=0.81873.

∴當(dāng)x=-0.2時(shí),多項(xiàng)式的值為0.818 73.

規(guī)律總結(jié) 利用秦九韶算法計(jì)算多項(xiàng)式的值,關(guān)鍵是能正確地將多項(xiàng)式改寫,然后由內(nèi)向外逐項(xiàng)計(jì)算.由于后項(xiàng)計(jì)算用到前項(xiàng)的結(jié)果,故應(yīng)認(rèn)真、細(xì)心,確保中間結(jié)果的準(zhǔn)確性.