Question

已知一元二次方程ax²+bx+c=0的两根的和为P,两根的平方和为q,两根的立方和为r,求ar+bq+cp

Answer 1

x1+x2=-b/a

x1*x2=c/a

p=x1+x2=-b/a

q=x1^2+x2^2=(x1+x2)^2-2x1*x2=b^2/a^2-2c/a

r=x1^3+x2^3=(x1+x2)*[(x1+x2)^2-3x1*x2]=-b^3/a^3+3bc/a^2

ar+bq+cp=a*(-b^3/a^3+3bc/a^2)+b*(b^2/a^2-2c/a)-bc/a=0