If P(x)=x3+ax2+bx+cP(x) = x^3 + ax^2 + bx + cP(x)=x3+ax2+bx+c has roots α,β,γ\alpha, \beta, \gammaα,β,γ, find the polynomial whose roots are α2,β2,γ2\alpha^2, \beta^2, \gamma^2α2,β2,γ2 in terms of a,b,ca, b, ca,b,c.
x3−(a2−2b)x2+(b2−2ac)x−c2x^3 - (a^2-2b)x^2 + (b^2-2ac)x - c^2x3−(a2−2b)x2+(b2−2ac)x−c2
x3+(a2−2b)x2+(b2−2ac)x+c2x^3 + (a^2-2b)x^2 + (b^2-2ac)x + c^2x3+(a2−2b)x2+(b2−2ac)x+c2
x3−(a2+2b)x2+(b2+2ac)x−c2x^3 - (a^2+2b)x^2 + (b^2+2ac)x - c^2x3−(a2+2b)x2+(b2+2ac)x−c2
x3−(a2−2b)x2+(b2+2ac)x+c2x^3 - (a^2-2b)x^2 + (b^2+2ac)x + c^2x3−(a2−2b)x2+(b2+2ac)x+c2