1 through 3 ask you to fill in some of the details of the analysis of the Lorenz equations in this section.(a) By solving Eq. (12) numerically, show that the real part of the complex roots changessign when r = 24.737.(b) Show that a cubic polynomial x3 + Ax2 + Bx + C has one real zero and two pureimaginary zeros only if AB = C.(c) By applying the result of part (b) to Eq. (12), show that the real part of the complexroots changes sign when r = 470/19.

F a, Lx *tr.r-)= x'-)xtZ l'(^)=tt>