請問高中數學---多項式有無更快算法?

2012-01-28 4:17 am
請問高中數學---多項式有無更快算法?
鉛筆算法是我自己用笨方法解的
答案是對
但覺得太笨了
請教各位大大有無更快解法?

圖片參考:http://imgcld.yimg.com/8/n/AC07731544/o/161201270590613872702050.jpg

回答 (1)

2012-01-28 5:01 am
✔ 最佳答案
Sol
f(x)=(x^35-6x^21+8x^13-5x^2-1)(x^9-2x^8+5x^3-x+1)
=a44x^44+a43x^43+…+a0
f(i)=(i^3-6i+8i-5i^2-1)*(i-2+5i^3-i+1)
=(-i-6i+8i+5-1)*(i-2-5i-i+1)
=(i+4)*(-5i-1)
=-5i^2-i-20i-4
=1-21i
f(i)=a^44i^44+a43i^43+a42i^42+a41i^41+a40i^40+a39i^39+a38i^38+a37i^37
+a36i^36+…+a3i^3+a2i^2+a1i+a0
=a^44-ia43-a42+ia41+a40-a39i-a38+ia37+a36+…-ia3-a^2+ia1+a0
=(a44-a42+a40-a38+…+a0)-i(a43-a41+a39-a37+…-a1)
=1-21i
a43-a41+a39-a37+…-a1=21
a1-a3+a5-…-a43=-21




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