Dla jakich parametrów p i q równanie x 3 + px + q = 0 ma pierwiastki x1, x2, x3 takie, że x1 = x2 = x3 + 6.

zamiast x1 napisze r  x1=r x2=r x3=r-6 [latex](x-r)^{2} (x-r+6)= x^{3} +px+q \ \ (x^{2} -2r+ r^{2} )(x-r+6)= x^{3} +px+q \ \ x^{3} -r x^{2} +6 x^{2} -2rx+2 r^{2} -12r+ r^{2} x- r^{3} +6 r^{2} =x^{3} +px+q \ \ x^{3}+ x^{2} (-r+6)+x(-2r+ r^{2} )+8 r^{2} -12r- r^{3} =x^{3} +px+q \ \ p=-2r+ r^{2} \ \ q=8 r^{2} -12r- r^{3}[/latex]