Given that the sum of the two of the quadratic equations AXX + BX + C = 0 is p, the sum of the squares of the two is Q, and the sum of the cubes of the two is r, find the value of Ar + BQ + CP It's a topic in the eighth grade summer exercise book Thank you!

Given that the sum of the two of the quadratic equations AXX + BX + C = 0 is p, the sum of the squares of the two is Q, and the sum of the cubes of the two is r, find the value of Ar + BQ + CP It's a topic in the eighth grade summer exercise book Thank you!

Let the roots of the equation be m, n
So am ^ 2 + BM + C = 0, an ^ 2 + BN + C = 0
So: AP + BQ + CR = a (m ^ 3 + n ^ 3) + B (m ^ 2 + n ^ 2) + C (M + n)
=m(am^2+bm+n)+n(an^2+bn+c)
=0+0
=0

Given that the sum of two of the quadratic equations ax & sup2; + BX + C = 0 is p, the sum of two squares is Q, and the sum of two cubes is r, find Ar + BQ + CP

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

If we know that the sum of the two squares of the quadratic equation AX + BX + C = 0 is p, the sum of the squares is Q, and the cube root is r, then Ar + BQ + CP =?
I hope some TC can help solve this problem

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